Sonata Bis Grant: m-syzygy plane curves

Research Team:

• Piotr Pokora (PI)

• Marek Janasz

• PhD position - TBD

The main research goals:

• constructions of m-syzygy plane curves

• constraints on weak-combinatorics of plane curves

• Numerical Terao's Conjecture and Ziegler/weak 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 and their interplay in algebra and combinatorics (Piotr Pokora), arXiv:2403:13377.

2. Constructions of curve arrangements using point-line operators (Piotr Pokora, Xavier Roulleau), arXiv:2403:20024.

3. Defect of irreducible plane curves with simple singularities (Piotr Pokora), arXiv:2404.03341.

4. On symmetric plane quartics (Marek Janasz), arXiv:2406.07015.

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

6. On the geography of log-surfaces (Bartosz Naskręcki, Piotr Pokora), in preparations.

Conferences:

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

• XXIV Coloquio Latinoamericano de Álgebra, 22-26 July 2024, Santiago (Chile), Invited Speaker - Piotr Pokora, Title of the talk: Rational curve arrangements: geometry and combinatorics.

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

Seminars:

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