Seminario Nacional de Geometría Algebraica en línea

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.

TPA

Julia Schneider, Université Bourgogne Europe

15 abril / 9:00 horas