Research Team:

• Piotr Pokora (PI)

• Marek Janasz (RI)

• Artur Bromboszcz (PhD)

The main research goals:

• constructions of m-syzygy plane curves,

• constraints on weak-combinatorics of plane curves,

• Numerical Terao's Conjecture and various Ziegler pairs,

• plus-one generated curves,

• understanding the defect of plane curves,

• geometric applications of m-syzygy plane curves,

• monodromy of rational plane curves.

Research papers:

1. Singular plane curves: freeness and combinatorics (Michael Cuntz, Piotr Pokora), Innovations in Incidence Geometry - Algebraic, Topological and Combinatorial 22(1): 47 - 65 (2025), Green Access AAM.

2. Defect of irreducible plane curves with simple singularities (Piotr Pokora), Annales Polonici Mathematici (Special Volume dedicated to A. Płoski) (2025). DOI:10.4064/ap240405-17-9, Green Access AAM.

3. On symmetric plane quartics (Marek Janasz), Taiwanese Journal of Mathematics 29(1): 1 - 11 (2025), Open Access with AAM.

4. Minimal plus-one generated line arrangements with double and triple intersection points (Artur Bromboszcz), International Journal of Mathematics Vol. 36, No. 11: Art Id. 2550040 (11 pages) (2025), DOI:10.1142/S0129167X25500405, Green Access AAM.

5. On the existence of maximizing curves of odd degrees (Marek Janasz, Izabela Leśniak), Proceedings of the American Mathematical Society, DOI:10.1090/proc/17335, Green Access AAM.

6. On Poincare polynomials for plane curves with quasi-homogeneous singularities (Piotr Pokora), Bulletin of the London Mathematical Society 57(8): 2549 - 2560 (2025), Green Access AAM.

7. On the addition technique for Betti and Poincare polynomials of plane curves (Piotr Pokora), Bulletin of the Polish Academy of Sciences - Mathematics 72(2): 111 - 118 (2024), Green Access AAM.

8. Constructions of curve arrangements using point-line operators (Piotr Pokora, Xavier Roulleau), arXiv:2403.20024, to appear in Experimental Mathematics, Green Access AAM.

9. On combinatorics of plus-one generated line arrangements (Artur Bromboszcz), arXiv:2411.17317, to appear in Bollettino dell'Unione Matematica Italiana, Open Access AAM.

10. On the geography of log-surfaces (Bartosz Naskręcki, Piotr Pokora), arXiv:2412.14635, to appear in EMS Surveys in Mathematical Sciences, Green Access AAM.

11. On free line arrangements with double, triple and quadruple points (Marek Janasz, Izabela Leśniak), arXiv:2504.05872, to appear in European Journal of Mathematics, Open Access AAM.

12. A new hierarchy for complex plane curves (Takuro Abe, Alex Dimca, Piotr Pokora), arXiv:241011470, to appear in the Canadian Mathematical Bulletin.

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

14. On homological properties of some Cynk-Szemberg octic hyperplane arrangements (Marek Janasz, Piotr Pokora), arXiv:2502.17031, under review.

15. Free line arrangements with low maximal multiplicity (Alexandru Dimca, Lukas Kuehne, Piotr Pokora), arXiv:2505.01733, under review.

16. On plus-one generated arrangements of conics (Artur Bromboszcz, Bartosz Jarosławski, Piotr Pokora), arXiv:2507.23024, under review. 

17. Addition theorems for Ziegler pairs of hyperplane arrangements (Takuro Abe, Lukas Kuhne, Piotr Pokora), arXiv:2509.19011, under review.

Conferences:

• Varieties with Boundries, 25 - 28 June 2024 Wakkanai (Japan), Invited Speaker - Piotr Pokora: "On the geography problem of log-surfaces".

• XXIV Coloquio Latinoamericano de Álgebra, 22-26 July 2024, Santiago (Chile), Invited Speaker Algebraic Geometry Session - Piotr Pokora: "Rational curve arrangements: geometry and combinatorics".

• 9. Forum Matematyków Polskich, 9 - 13 września 2024, Katowice, GKLW session Invited Speaker - Piotr Pokora: "Defect of irreducible plane curves with simple singularities".

• XLV Konferencja i Warsztaty "Geometria Analityczna i Algebraiczna", Łódź, 6 - 10 January 2025 - Artur Bromboszcz: "Combinatorial properties of plus-one generated line arrangements" and Piotr Pokora: "Poincare polynomials for curve arrangements".

• Geometry of Arrangements Mini-Workshop, Hannover, 20 - 21 March 2025, Invited Speaker - Piotr Pokora: "Poincare polynomials of plane curves with quasi-homogeneous singularities.

• New Perspectives on Hyperplane Arrangements, Bochum, 12 - 16 May 2025, Invited Speaker - Piotr Pokora: "A new hierarchy for line arrangements".

• Summer Institute School Algebraic Geometry, Fort Collins (Colorado USA), 14 - 18 July 2025, Invited Contributed Talk Speaker - Piotr Pokora: "Free curves in algebraic geometry".

External Seminars:

• Moduli and Friends ZOOM Seminar, 20th May 2024 (Bucharest): Talk: Constructions of free arrangements using point-line operators by Piotr Pokora.