Fourier-Mukai equivalences arising from Cremona transformations

Abstract: It is widely conjectured that a cubic fourfold is rational if and only if its derived category contains a summand that comes from a K3 surface. This question suggests the study about how the birational geometry of cubic fourfolds is determined by their associated K3 surfaces, or more generally, by their K3 categories. This talk aims to introduce two examples of equivalences between K3 categories constructed from Cremona transformations, i.e., birational automorphisms of projective spaces, as well as some of their applications.

Mathematics

Audience: researchers in the topic

ICCM 2020