Seminario Nacional de Geometría Algebraica en línea

Seminario virtual, IMUNAM, Oaxaca
Miércoles 8 y 15 de abril de 2026 a las 15:00 horas
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https://www.matem.unam.mx/~lozano/eseminar.html

Cubic fourfolds with many Fourier Mukai partners

Lisa Marquand, NYU

8 abril / 15:00 horas

Resumen: Two cubic fourfolds are Fourier Mukai partners if there is an equivalence between their Kuznetsov components. It has been suggested by Huybrechts that a pair of Fourier Mukai cubic fourfold partners are birational; however, examples of such phenomena are rare.

In an attempt to investigate this phenomena, we develop an algorithm for counting the number of Fourier Mukai partners of a given cubic fourfold and run it on cubics with automorphisms. We prove that a cubic fourfold admitting a symplectic involution has 1120 non-trivial Fourier-Mukai partners, all birational but non-isomorphic. We'll explain the 1120 in terms of root systems and non-syzygetic pairs of cubic scrolls.

Atomic semi-orthogonal decompositions for derived categories of G-surfaces

Julia Schneider, Université Bourgogne Europe

15 abril / 9:00 horas

Resumen: In this talk, I discuss a joint work with Alexey Elagin and Evgeny Shinder that lies at the intersection of birational and derived geometry. What kind of geometric information is encoded in the derived category of a variety, and how does this information behave under birational maps?

We consider the case of surfaces equipped with a group action, and show that their derived categories admit a canonical (mutation-equivalence class of) semi-orthogonal decomposition that "behaves well" with respect to birational geometry. We call such decompositions "atomic". If time permits, I will discuss applications to (bi-)rationality questions.

This talk is intended for non-experts; all notions will be explained.

Seminario Nacional de Geometría Algebraica en línea

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