Derived categories of cubic fourfolds and their geometric applications

Derived categories of cubic fourfolds and their geometric applications

Alex Perry (Columbia, Mathematics)

Wednesday, January 15, 2020 -
12:00pm to 1:00pm
Location: 
119 Physics

A fundamental problem in algebraic geometry is to determine whether a given algebraic variety is birational to projective space. This is most prominently open for cubic fourfolds, i.e. hypersurfaces defined by a cubic polynomial in a five-dimensional projective space. A decade ago, Kuznetsov suggested an approach to this problem using the derived category of coherent sheaves. I will explain recent applications of this perspective to fundamental questions in hyperkahler geometry and Hodge theory, which in turn shed light on the original question about cubic fourfolds.

Last updated: 2020/02/22 - 6:38am