Papers and preprints

All 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. 

Monographs:

1. Wybrane zagadnienia teorii krzywych płaskich (Monography in Polish), Wydawnictwo Naukowe Uniwersytetu Pedagogicznego, Prace Monograficzne 1130, pp. 92, 2022, Open Access.

Published articles:

1. Rank Function Equations (with M. Skrzyński), Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica vol. 11: 101 - 109 (2012), Open Access.

2. 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.

3. Rank Function Equations and their solution sets,  Miskolc Mathematical Notes 15(2): 651 - 663 (2014), Open Access.

4. 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.

5. Bounded Negativity and Arrangements of Lines (with Th. Bauer, S. Di Rocco, B. Harbourne, J. Huizenga, A. Lundman, T. Szemberg), International Mathematical Research Notes 2015, 9456 - 9471 (2015), Open Access.

6. Numerical and enumerative results on Okounkov bodies, British Journal of Mathematics and Computer Sciences 9(2): 112 - 121 (2015), Open Access.

7. 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.

8. 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.

9. Harbourne constants and arrangements of lines on hypersurfaces in P^{3}, Taiwanese Journal of Mathematics vol. 20(1) : 25 - 31 (2016), Open Access.

10. Harbourne constants and conic configurations on the projective plane (with H. Tutaj-Gasińska), Mathematische Nachrichten 289(7): 888 - 894 (2016), Green Access.

11. 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.

12. Hirzebruch type inequalities and plane curve configurations, International Journal of Mathematics vol. 28(2): 1750013 (11 pages) (2017), Green Access.

13. The orbifold Langer-Miyaoka-Yau inequality and Hirzebruch-type inequalities, Electronic Research Announcements in Mathematical Sciences vol. 24: 21 - 27 (2017), Open Access.

14. On line and pseudoline configurations and ball-quotients (with J. Bokowski),  Ars Mathematica Contemporanea 13(2): 409 - 416 (2017), Open Access.

15. 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.

16. 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.

17. 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.

18. On the Sylvester-Gallai and the orchard problem for pseudoline arrangements (with J. Bokowski), Periodica Mathematica Hungarica 77(2): 164 -174 (2018), Green Access.

19. Curve configurations in the projective plane and their characteristic numbers (with Adam Czapliński). Phenomenological Approach to Algebraic Geometry Banach Center Volume 116, pp. 63 - 76 (2018), Green Access.

20. Hirzebruch-Kummer covers of algebraic surfaces, Turkish Journal of Mathematics 43(1): 412 - 421 (2019), Open Access.

21. Harbourne constants under ramified morphisms (with Joaquim Roe), Results in Mathematics 74(3): Article #109 (2019), Open Access.

22. Seshadri constants and special point configurations in the projective plane, Rocky Mountain Journal of Mathematics 49(3): 963 - 978 (2019), Green Access.

23. 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.

24. On Seshadri constants and point-curve configurations (with Marek Janasz), Electronic Research Archive 28(2): 795 - 805 (2020), Open Access.

25. 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.

26. Hirzebruch-type inequalities viewed as tools in combinatorics, Electronic Journal of Combinatorics 28(1): #P1.9 (2021), Open Access.

27. The 21 reducible polars of Klein's quartic (with Joaquim Roe), Experimental Mathematics 30(1): 1 - 18 (2021), Green Access.

28. 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.

29. On 3-syzygy and unexpected plane curves (with Grzegorz Malara and Halszka Tutaj-Gasińska), Geometriae Dedicata 214(1): 49 - 63 (2021), Open Access.

30. Algebraic poperties of Levi graphs associated with arrangements (with Tim Roemer), Research in the Mathematical Sciences 9: ID 30 - 17 pages (2022), Open Access.

31. 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.

32. 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.

33. Some special triple covers of algebraic surfaces (with Nicolina Istrati and Soenke Rollenske), Documenta Mathematica 27: 2301 - 2332 (2022), Open Access.

34. Q-conic arrangements in the complex projective plane, Proceedings of the American Mathematical Society 151(7): 2873 - 2880 (2023), Green Access.

35. Conic-line arrangements in the complex projective plane (with Tomasz Szemberg), Discrete and Computational Geometry 69(4): 1121 - 1138 (2023), Green Access.

36. Maximizing curves viewed as free curves (with Alex Dimca), International Mathematical Research Notes 2023 (22): 19156 - 19183 (2023), Green Access.

37. 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.

38. Klein's arrangements of conics and lines (with Gabor Gevay), Beiträge zur Algebra und Geometrie 65(2): 393 - 414 (2024), Green Access.

39. 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.

40. 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.

41. 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.

42. Addition-deletion results for plus-one generated curves (with Anca Macinic), arXiv:2310.19610, to appear in Journal of Algebraic Combinatorics, Open Access.

43. Hunting for Miyaoka-Kobayashi curves (with Alex Dimca), arXiv:2209.14846, to appear in Publications of the Research Institute for Mathematical Sciences (PRIMS) (2025), Green Access.

44. Construction of free curves by adding hyperosculating conics to a given curve (with Alex Dimca, Giovanna Ilardi and Grzegorz Malara), arXiv:2311.08913, Green Access.

45. On the Boucksom-Zariski decomposition for Irreducible Holomorphic Symplectic Varieties and bounded negativity (with Michał Kapustka, Giovanni Mongardi, and Gianluca Pacienza), arXiv.org:1911.03367, Green Access.

Preprints:

1. On the Alexander polynomials of conic-line arrangements (with Alex Dimca and Gabriel Sticlaru), arXiv:2305.01450, under review.

2. On arrangements of smooth plane quartics and lines (with Marek Janasz and Marcin Zielinski), arXiv:2308.16514, under review.

3. On plus-one generated conic-line arrangements with simple singularities (with Anca Macinic), arXiv:2309.14228, under review.

4. Freeness of arrangements of lines and a conic with ordinary quasi-homogeneous singularities, arXiv:2312.13052, under review

5. Bounds for characteristic numbers of conic-line arrangements in the plane (with Rita Pardini), arXiv:2312.12950, under review.

6. Singular plane curves and their interplay in algebra and combinatorics (expository paper with new ideas), arXiv:2403:13377, under review.

7. Constructions of curve arrangements using point-line operators (with Xavier Roulleau), arXiv:2403:20024, under review.

8. Defect of irreducible plane curves with simple singularities, arXiv:2404.03341, under review.

9. On the Numerical Terao's Conjecture and Ziegler pairs for line arrangements (with Dante Luber and Lukas Kuhne), arXiv:2407.07070, under review.

Chapters in collective monographs:

1. 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). 

2. Conic-line arrangements in the complex projective plane, ZAG’s Handbook of Modern Algebraic Geometry, Chapman&Hall CRC, to appear.

MFO Reports:

1. Mini-Workshop: 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.

2. 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.

3. Workshop: Lefschetz Properties in Algebra, Geometry and Combinatorics. Talk: Unexpectedly found unexpected curves. Report No. 31/2020: 36 - 39,  DOI: 10.4171/OWR/2020/31.

4. 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.

Comments on 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.