Zespół / Team:

• Piotr Pokora (PI)

• Grzegorz Malara

• Paulina Wiśniewska (PhD scholarship)

Główne cele projektu / Main goals of the project:

1. Develop the theory of curve arrangements in algebraic surfaces,

2. Surfaces of general type, log surfaces of general type with small / large volumes,

3. Freeness of divisors,

4. Hirzebruch-type inequalities,

5. Examples of algebraic curves with certain extreme properties.

Publikacje / Papers:

1. On Seshadri constants and point-curve configurations (Piotr Pokora and Marek Janasz), Electronic Research Archive 28(2): 795 - 805 (2020), (Open Access, IF: 1,833).

2. On submaximal curves in fake projective planes (Piotr Pokora and Halszka Tutaj-Gasińska), Journal of Pure and Applied Algebra 225(10): ID 106709 - 9 pages (2021), (IF: 0,834).

3. On 3-syzygy and unexpected plane curves (Grzegorz Malara, Piotr Pokora, and Halszka Tutaj-Gasińska), Geometriae Dedicata 214(1): 49 - 63 (2021), (Open Access, IF: 0,516).

4. On conic-line arrangements with nodes, tacnodes, and ordinary triple points (Alexandru Dimca and Piotr Pokora), Journal of Algebraic Combinatorics 56(2): 403 - 424 (2022), (Open Access, IF: 0,800).

5. On plane conic arrangements with nodes and tacnodes (Alexandru Dimca, Marek Janasz, and Piotr Pokora),  Innovations in Incidence Geometry - Algebraic, Topological and Combinatorial 19(2): 47 - 58 (2022), (Green Access, IF: 0,000).

6. Some special triple covers of algebraic surfaces (with Nicolina Istrati and Soenke Rollenske), Documenta Mathematica 27: 2301 - 2332 (2022), (Open Access, IF: 0,900).

7. Generic projections of the H_4 configuration of points (Maciej Zięba and Paulina Wiśniewska),  Advances in Applied Mathematics 142: ID Article 102432 (2023), (Open Access, IF:1,100).

8. Q-conic arrangements in the complex projective plane, Proceedings of the American Mathematical Society 151(7): 2873 - 2880 (2023), (Green Access, IF: 1,000).

9. Conic-line arrangements in the complex projective plane (Piotr Pokora and Tomasz Szemberg), Discrete and Computational Geometry 69(4): 1121 - 1138 (2023), (Green Access, IF: 0,800).

10. A note on free determinantal hypersurface arrangements in P^14 (Marek Janasz and Paulina Wiśniewska), Proyecciones Journal of Mathematics 42(4): 1093 - 1104 (2023), (Open Access, IF: 0,000).

11. Maximizing curves viewed as free curves (with Alex Dimca), International Mathematical Research Notes 2023 (22): 19156 -- 19183 (2023), (Green Access, IF: 1,000).

12. 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, IF: 2.200).

13. Klein's arrangements of conics and lines (with Gabor Gevay), Beiträge zur Algebra und Geometrie 65(2): 393 – 414 (2024), (Green Access, IF: 0.500).

14. Unexpected properties of the Klein configuration of 60 points in P^3 (with Justyna Szpond and Tomasz Szemberg), Michigan Math. Journal (2023) (ahead of print), (Green Access, IF: 0,900).

15. Regularity and symbolic defect of points on rational normal curves (Iman Bahmani Jafarloo and Grzegorz Malara), Periodica Math. Hungarica (2023) (ahead of print), (Open Access, IF: 0,800).

16. Hunting for Miyaoka-Kobayashi curves (with Alex Dimca), arXiv:2209.14846, to appear in Publications of the Research Institute for Mathematical Sciences (PRIMS) (2023), (Green Access, IF: 1.200).

17. On unexpected curves of type (d+k,d) (Grzegorz Malara and Halszka Tutaj-Gasińska),  arXiv:2109.00769,  to appear in The Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (Green Access, IF: 1,400)

Monografie / Monographs:

1. P. Pokora, Wybrane zagadnienia teorii układów krzywych płaskich, Wydawnictwo Naukowe Uniwersytetu Pedagogicznego w Krakowie, Prace Monograficzne 1130, pp. 92, 2022.

Wydarzenia / Events:

• Konferencja i Warsztaty Geometria Algebraiczna i Analityczna, 7 - 10 stycznia 2020 (Talk: Piotr Pokora, On the weighted bounded negativity conjecture).

• NoGAGS Hannover, 29 - 31 January 2020 (Piotr Pokora).

• Winter School "Geometry, Algebra and Combinatorics of Moduli Spaces and Configurations, Toblach, 24 - 28 February 2020 (Piotr Pokora).

• Research Visit in Santiago Chile (Santiago Chile), Giancarlo Urzua, 13 - 21 March 2020, (Piotr Pokora, SANTAS seminar talk) -- cancelled due to COVID-19.

• Edge Online Seminar, University of Edinburgh, 28th March 2020 (Talk: Piotr Pokora, Conic-line arrangements in the complex projective plane).

• Arrangements at Home II, West Ontario, Worldwide ZOOM Workshop, 11 - 12 June 2020 (Talk: Piotr Pokora, Conic-line arrangements in the plane).

• Complex and symplectic curve arrangements (organizers: Marco Golla, Piotr Pokora, Laura Starkston), Djursholm, 13 - 17 July, 2020 - A reincarnation took place in Nantes in December 2023.

• Oberwolfach Research Fellowship (Research in Pairs in the COVID times), MFO Oberwolfach, 13 - 26 September 2020.

• Lefschetz Properties in Algebra, Combinatorics and Geometry (Workshop), MFO Oberwolfach, 27 September - 3 October 2020 (Talk: Piotr Pokora, Unexpectedly found unexpected curves).

• 17th Virtual Seminar on Commutative Algebra and Related Topics, 6-8 January 2021, Teheran (via Google Meet).

• Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications, MFO Oberwolfach, 24 - 30 January 2021 (Talk: Piotr Pokora, Unexpected curves and line arrangements.)

• 8 ECM Slovenia (but online), 20-26 June 2021, Minisymposia Invited Speaker MS-ID 81 Configurations, (Talk: Piotr Pokora, Hirzebruch-type inequalities and extreme point-line configurations).

• Konferencja i Warsztaty Geometria Algebraiczna i Analityczna, 10 - 14 stycznia 2021 (Talk: Paulina Wiśniewska, Stałe Waldschmidta symetrycznych układów punktów).

• Effective Methods in Algebraic Geometry 2022, 20-24 June 2022, Kraków (Organizing Committee: Piotr Pokora, Talk: Paulina Wiśniewska, On H_4 configuration of points in PP^3).

• Real algebraic geometry and singularities. Conference in honor of Wojciech Kucharz's 70th birthday,  10 - 17 September 2022, Kraków (Talk: Piotr Pokora, Nearly-free and free plane curves).

• EDGE 2022, 21 - 25 November 2022, ICMS Edinburgh (Talk: Piotr Pokora, Maximizing Curves). 

• Conference/Workshop Complex and Symplectic curves, 12-16 December 2022, Nantes (Organizing Committee: Piotr Pokora).

• XLIII Konferencja Geometria Analityczna i Algebraiczna, 9-13 January 2023, Łódź (Talk: Piotr Pokora, Maksymalizujące krzywe płaskie).