Embedded Files
Wybrane zagadnienia teorii krzywych płaskich, Wydawnictwo Naukowe Uniwersytetu Pedagogicznego, Prace Monograficzne 1130, pp. 92, 2022, Open Access.
Poniżej wersja poprawiona (usunięto literówki):
Uklady_Hiperplaszczyzn.pdfAll arXiv papers available here or please see my ResearchGate. It might happen that the final versions of articles are slightly different than those from arXiv. The latest versions on demand.
Published articles:
Early View/Accepted for Publication:
Published articles:
- Rank Function Equations (with M. Skrzyński), Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica vol. 11: 101 - 109 (2012), Open Access.
- Points Fattening on P^1 x P^1 and symbolic powers of bihomogeneous ideals (with M. Baczyńska, M. Dumnicki, A. Habura, G. Malara, T. Szemberg, J. Szpond, H. Tutaj-Gasińska), Journal of Pure and Applied Algebra 218: 1555 - 1562 (2014), Green Access.
- Rank Function Equations and their solution sets, Miskolc Mathematical Notes 15(2): 651 - 663 (2014), Open Access.
- Minkowski bases on algebraic surfaces with rational polyhedral pseudoeffective cone (with T. Szemberg), Electronic Research Announcements in Mathematical Sciences vol. 21, 126 - 131 (2014), Open Access.
- Bounded Negativity and Arrangements of Lines (with Th. Bauer, S. Di Rocco, B. Harbourne, J. Huizenga, A. Lundman, T. Szemberg), International Mathematical Research Notices 2015, 9456 - 9471 (2015), Open Access.
- Numerical and enumerative results on Okounkov bodies, Journal of Advances in Mathematics and Computer Science 9(2): 112 - 121 (2015), Open Access.
- Minkowski decomposition and generators of the moving cone for toric varieties (with D. Schmitz and S. Urbinati), Quarterly Journal of Mathematics 66(3): 925 - 939 (2015), Green Access.
- On integral Zariski Decompositions of pseudoeffective integral divisors on algebraic surfaces (with B. Harbourne and H. Tutaj-Gasińska), Electronic Research Announcements in Mathematical Sciences vol. 22: 103 - 108 (2015), Open Access.
- Harbourne constants and arrangements of lines on hypersurfaces in P^3, Taiwanese Journal of Mathematics vol. 20(1) : 25 - 31 (2016), Open Access.
- Harbourne constants and conic configurations on the projective plane (with H. Tutaj-Gasińska), Mathematische Nachrichten 289(7): 888 - 894 (2016), Green Access.
- A counterexample to the containment I^(3) ⊂ I^2 over the reals (with A. Czapliński, A. Główka, G. Malara, M. Lamba-Baczyńska, P. Łuszcz-Świdecka, J. Szpond), Advances in Geometry vol. 16(1): 77 - 82 (2016), Green Access.
- Hirzebruch type inequalities and plane curve configurations, International Journal of Mathematics vol. 28(2): 1750013 (11 pages) (2017), Green Access.
- The orbifold Langer-Miyaoka-Yau inequality and Hirzebruch-type inequalities, Electronic Research Announcements in Mathematical Sciences vol. 24: 21 - 27 (2017), Open Access.
- On line and pseudoline configurations and ball-quotients (with J. Bokowski), Ars Mathematica Contemporanea 13(2): 409 - 416 (2017), Open Access.
- Bounded negativity, Harbourne constants and transversal arrangements of curves (with X. Roulleau and T. Szemberg), Annales de l'Institut Fourier Grenoble 67(6): 2719 - 2735 (2017), Open Access.
- On the boundedness of the denominators in the Zariski decomposition on surfaces (with Th. Bauer and D. Schmitz), Journal fur die reine und angewandte Mathematik 733(12): 251 - 259 (2017), Green Access.
- On the local negativity of surfaces with numerically trivial canonical class (with R. Laface), Rendiconti Lincei – Matematica e Applicazioni 29: 237 - 253 (2018), Green Access.
- On the Sylvester-Gallai and the orchard problem for pseudoline arrangements (with J. Bokowski), Periodica Mathematica Hungarica 77(2): 164 - 174 (2018), Green Access.
- Curve configurations in the projective plane and their characteristic numbers (with Adam Czapliński), Phenomenological Approach to Algebraic Geometry Banach Center Volume 116: 63 - 76 (2018), Green Access.
- Hirzebruch-Kummer covers of algebraic surfaces, Turkish Journal of Mathematics 43(1): 412 - 421 (2019), Open Access.
- Harbourne constants under ramified morphisms (with Joaquim Roe), Results in Mathematics 74(3): Article #109 (2019), Open Access.
- Seshadri constants and special point configurations in the projective plane, Rocky Mountain Journal of Mathematics 49(3): 963 - 978 (2019), Green Access.
- Local negativity of surfaces with non-negative Koidara dimension and transversal configurations of curves (with R. Laface), Glasgow Mathematical Journal 62(1): 123 - 135 (2020), Green Access.
- On Seshadri constants and point-curve configurations (with Marek Janasz), Electronic Research Archive 28(2): 795 - 805 (2020), Open Access.
- Towards the weighted bounded negativity conjecture for blow-ups of algebraic surfaces (with R. Laface), Manuscripta Mathematica 163(3-4): 361 - 373 (2020), Open Access.
- Hirzebruch-type inequalities viewed as tools in combinatorics, Electronic Journal of Combinatorics 28(1): #P1.9 (2021), Open Access.
- The 21 reducible polars of Klein's quartic (with Joaquim Roe), Experimental Mathematics 30(1): 1 - 18 (2021), Green Access.
- On submaximal curves in fake projective planes (with Halszka Tutaj-Gasińska), Journal of Pure and Applied Algebra 225(10): ID 106709 - 9 pages (2021), Green Access.
- On 3-syzygy and unexpected plane curves (with Grzegorz Malara and Halszka Tutaj-Gasińska), Geometriae Dedicata 214(1): 49 - 63 (2021), Open Access.
- Algebraic poperties of Levi graphs associated with arrangements (with Tim Roemer), Research in the Mathematical Sciences 9: ID 30 - 17 pages (2022), Open Access.
- On plane conic arrangements with nodes and tacnodes (with Alexandru Dimca and Marek Janasz), Innovations in Incidence Geometry - Algebraic, Topological and Combinatorial 19(2): 47 - 58 (2022), Green Access.
- On conic-line arrangements with nodes, tacnodes, and ordinary triple points (with Alexandru Dimca), Journal of Algebraic Combinatorics 56(2): 403 - 424 (2022), Open Access.
- Some special triple covers of algebraic surfaces (with Nicolina Istrati and Soenke Rollenske), Documenta Mathematica 27: 2301 - 2332 (2022), Open Access.
- Q-conic arrangements in the complex projective plane, Proceedings of the American Mathematical Society 151(7): 2873 - 2880 (2023), Green Access.
- Conic-line arrangements in the complex projective plane (with Tomasz Szemberg), Discrete and Computational Geometry 69(4): 1121 - 1138 (2023), Green Access.
- Maximizing curves viewed as free curves (with Alex Dimca), International Mathematical Research Notices 2023 (22): 19156 - 19183 (2023), Green Access.
- Construction of free curves by adding lines to a given curve (with Alex Dimca, Giovanna Ilardi, and Gabriel Sticlaru), Results in Mathematics 79: Art. Id 11, 31 pages (2024), Open Access.
- Klein's arrangements of conics and lines (with Gabor Gevay), Beiträge zur Algebra und Geometrie 65(2): 393 - 414 (2024), Green Access.
- On free and nearly free arrangements of conics admitting certain ADE singularities, Annali dell'Università di Ferrara 70(3): 593 - 606 (2024), EDGE Volume 2018 - 2022, Open Access.
- On K-stability of P^3 blown up along a quintic elliptic curve (with Ivan Cheltsov), Annali dell'Università di Ferrara 70(3): 1165 - 1192 (2024), EDGE Volume 2018 - 2022, Open Access.
- Unexpected properties of the Klein configuration of 60 points in P^3 (with Justyna Szpond and Tomasz Szemberg), Michigan Math. Journal 74(3): 599 - 615 (2024), Green Access.
- Addition-deletion results for plus-one generated curves (with Anca Macinic), Journal of Algebraic Combinatorics 60(3): 723 - 734 (2024), Green Access.
- On plus-one generated conic-line arrangements with simple singularities (with Anca Macinic), Rendiconti Lincei – Matematica e Applicazioni 35(3): 349 - 364 (2024), Open Access.
- On the addition technique for Betti and Poincare polynomials of plane curves, Bulletin of the Polish Academy of Sciences - Mathematics 72(2): 111 - 118 (2024), Green Access.
- Construction of free curves by adding hyperosculating conics to a given curve (with Alex Dimca, Giovanna Ilardi and Grzegorz Malara), International Mathematical Research Notices Vol. 2025(1): Art Id. rnae273, 12 pages (2025), Green Access.
- On arrangements of smooth plane quartics and lines (with Marek Janasz and Marcin Zieliński), Fundamenta Mathematicae 268(2) : 151 - 170 (2025), Green Access.
- Singular plane curves: freeness and combinatorics (with Michael Cuntz), Innovations in Incidence Geometry - Algebraic, Topological and Combinatorial 22(1): 47 - 65 (2025), Green Access.
- Hunting for Miyaoka-Kobayashi curves (with Alex Dimca), Publications of the Research Institute for Mathematical Sciences 61(3): 315 - 333 (2025), Open Access.
- Freeness of arrangements of lines and one conic with ordinary quasi-homogeneous singularities, Taiwanese Journal of Mathematics - Special Volume dedicated to Yuri Prokhorov 29(6): 1651 - 1666 (2025), Open Access.
- On Poincare polynomials for plane curves with quasi-homogeneous singularities, Bulletin of the London Mathematical Society 57(8): 2549 - 2560 (2025), Green Access.
- Defect of irreducible plane curves with simple singularities, Annales Polonici Mathematici - Special Volume dedicated to Arkadiusz Płoski 135: 295 - 303 (2025), Green Access.
- On plus-one generated arrangements of conics (with Artur Bromboszcz and Bartosz Jarosławski), Geometriae Dedicata 220: Art Id. 10, 15 pages (2026), Open Access.
- On the Boucksom-Zariski decomposition for Irreducible Holomorphic Symplectic Varieties and bounded negativity (with Michał Kapustka, Giovanni Mongardi, and Gianluca Pacienza), Bulletin de la Société Mathématique de France 154(1): 107 - 134 (2026), Open Access.
- Free line arrangements with low maximal multiplicity (with Alexandru Dimca and Lukas Kuhne), Journal of Algebraic Combinatorics 63(3): Art. Id. 45, 19 pages (2026), Green Access.
- On homological properties of some Cynk-Szemberg octic hyperplane arrangements (with Marek Janasz), Journal of the Korean Mathematical Society 63(4): 753 - 771 (2026), Open Access.
- A new hierarchy for complex plane curves (with Takuro Abe and Alex Dimca), Canadian Mathematical Bulletin 68(3): - (2026), Green Access.
- Bounds for characteristic numbers of conic-line arrangements in the plane (with Rita Pardini), Collectanea Mathematica 77(3): 815 - 826 (2026), Open Access.
- On combinatorial bounds for the total Tjurina numbers of certain curves and surfaces with isolated singularities, Mathematische Nachrichten 299(10): - (2026), Open Access.
Early View/Accepted for Publication:
- On M-arrangements of conics and lines with ordinary singularities (with Marek Janasz), TBAS (2026), Green Access.
- On the Numerical Terao's Conjecture and Ziegler pairs for line arrangements (with Dante Luber and Lukas Kuehne), Journal of Commutative Algebra (2026), Green Access.
- On the geography of log-surfaces (with Bartosz Naskręcki), EMS Surveys in Mathematical Sciences (202X), Green/Open Access.
- Constructions of curve arrangements using point-line operators (with Xavier Roulleau), Experimental Mathematics (202X), Green Access.
- On the Alexander polynomials of conic-line arrangements (with Alex Dimca and Gabriel Sticlaru), Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (2028), Green Access.
Preprints:
- Addition theorems for Ziegler pairs of hyperplane arrangements (with Takuro Abe and Lukas Kuhne), arXiv:2509.19011, under review.
- On the Jacobian algebras of Ziegler pairs of plane arrangements (with Alex Dimca), arXiv:2604.25637, under review.
- A Pascal-type construction of the Segre cubic and the Cremona-Richmond configuration (with Tomasz Szemberg), arXiv:2606.18387, under review.
- On Ziegler pairs of line arrangements: from non-existence to abundance (with Alex Dimca), arXiv:2606.20421, under review.
- A nine-line counterexample to a conjecture on the minimal degree of Jacobian relations (with Alex Dimca), arXiv:2607.01985, under review.
- A (24_4,32_3)-configuration on the Schur quartic with logarithmic Chern slope 14/5 (with Bartosz Naskrecki), arXiv:2607.07898, under review.
- A counterexample to Purdy’s inequality for hyperplane arrangements in projective three-space (with Mateusz Michałek), arXiv:2607.08463, under review.
- On the Numerical Terao Conjecture, arXiv:2608.05662, under review.
- Simplicial arrangements in real projective three-space revisited (with Marek Janasz), arXiv:2608.28254.
- Demailly's Inequality for Finite Sets of Points in Positive Characteristic (with Tomasz Szemberg), arXiv:2609.
Chapters in Collective Monographs:
- Extremal properties of line arrangements in the complex projective plane. Krasiński, Tadeusz (ed.) et al., Analytic and algebraic geometry 3. In remembrance of Jacek Chądzyński and on the occasion of the 70th birthdays of Tadeusz Krasiński and Andrzej Nowicki. Łódź: Łódź University Press. 191-200 (2019).
- Conic-line arrangements in the complex projective plane, ZAG’s Handbook of Modern Algebraic Geometry, Chapman and Hall CRC, Art Id. 164 (2025).
MFO Reports:
- Mini-Workshop: Negative Curves on Algebraic Surfaces. Talk: Real counterexample to the containment I^(3) ⊂ I^2 and line arrangements. Report No. 10/2014: 566 - 567 (2014), DOI: 10.4171/OWR/2014/10.
- Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry. Talk: Local Negativity, Curve Arragements and Harbourne constants. Report No. 14/2016: 685 - 687 (2016), DOI: 10.4171/OWR/2016/14.
- Workshop: Lefschetz Properties in Algebra, Geometry and Combinatorics. Talk: Unexpectedly found unexpected curves. Report No. 31/2020: 36 - 39 (2020), DOI: 10.4171/OWR/2020/31.
- Conference: Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications. Talk: Unexpected curves and line arrangements. Report No. 5/2021: 56 - 59 (2021), DOI: 10.4171/OWR/2021/5.
Additions to published papers:
Addendum to Harbourne constants and conic configurations on the projective plane
At the end of page 892 we discuss (really sketch) positivity of K'. It is quite easy to see that K' can be rewritten as an effective divisor using only the exceptional divisors and the strict transforms of irreducible components of our configuration. Indeed, if n = 2 we can observe that K' is nef, especially for a configuration of 4 curves of bidegree (1, 1) and 12 double points one has (K')^2 = 0 and e(Y) = 12. If now n >= 3, then using standard considerations we can show that K' is big and nef - in the paper we wrote that K' is ample. However, and fortunately, in this particular case this might be viewed as a typo since our idea was to emphasize only positivity of K' and the fact that our surface Y is of general type in order to apply the Bogomolov-Miyaoka-Yau inequality, and it does not interfere on the main result.
Addendum to On conic-line arrangements with nodes, tacnodes, and ordinary triple points
There is a second projectively inequivalent realization of the weak combinatorics
(d,k;n_2,t,n_3)=(3,2;0,5,3).
Consider the two smooth conics
Q_1 : z^2 + xy = 0
and
Q_2 : (y-x-z)^2 + xy =0,
together with the three lines
L_1 : x=0,L_2 : y=0,L_3 : x-y=0.
Hence the corresponding conic-line arrangement is defined by
\mathcal{CL}'\colon f=0,
where f is the product of the above 5 equations.
The arrangement \mathcal{CL}' has exactly five tacnodes and three ordinary triple points, and no nodes. Moreover, it is free with exponents (3,3). In contrast to the previously considered realization, where the three lines form a triangle, the lines L_1, L_2, L_3 are concurrent at (0:0:1). Since concurrency is preserved under projective transformations, these two realizations are not projectively equivalent. This means that there is the second branch in Theorem 5.7(4) and this particular weak combinatorics does not determine the arrangement up to the projective equivalence.This ommision does not touch other results obtained in the paper.
Addendum to Harbourne constants and conic configurations on the projective plane
At the end of page 892 we discuss (really sketch) positivity of K'. It is quite easy to see that K' can be rewritten as an effective divisor using only the exceptional divisors and the strict transforms of irreducible components of our configuration. Indeed, if n = 2 we can observe that K' is nef, especially for a configuration of 4 curves of bidegree (1, 1) and 12 double points one has (K')^2 = 0 and e(Y) = 12. If now n >= 3, then using standard considerations we can show that K' is big and nef - in the paper we wrote that K' is ample. However, and fortunately, in this particular case this might be viewed as a typo since our idea was to emphasize only positivity of K' and the fact that our surface Y is of general type in order to apply the Bogomolov-Miyaoka-Yau inequality, and it does not interfere on the main result.
Addendum to On conic-line arrangements with nodes, tacnodes, and ordinary triple points
There is a second projectively inequivalent realization of the weak combinatorics
(d,k;n_2,t,n_3)=(3,2;0,5,3).
Consider the two smooth conics
Q_1 : z^2 + xy = 0
and
Q_2 : (y-x-z)^2 + xy =0,
together with the three lines
L_1 : x=0,L_2 : y=0,L_3 : x-y=0.
Hence the corresponding conic-line arrangement is defined by
\mathcal{CL}'\colon f=0,
where f is the product of the above 5 equations.
The arrangement \mathcal{CL}' has exactly five tacnodes and three ordinary triple points, and no nodes. Moreover, it is free with exponents (3,3). In contrast to the previously considered realization, where the three lines form a triangle, the lines L_1, L_2, L_3 are concurrent at (0:0:1). Since concurrency is preserved under projective transformations, these two realizations are not projectively equivalent. This means that there is the second branch in Theorem 5.7(4) and this particular weak combinatorics does not determine the arrangement up to the projective equivalence.This ommision does not touch other results obtained in the paper.
Google Sites
Report abuse