The BGMN conjecture via windows and stable pairs

Abstract: Let C be a smooth projective curve of genus at least 2 and let N be the moduli space of stable rank-two bundles on C of odd degree. We construct a semi-orthogonal decomposition in the derived category of N conjectured by Narasimhan and by Belmans, Galkin and Mukhopadhyay. It contains two copies of the i-th symmetric power of C for i=0,...,g-2, one copy of the (g-1)-st symmetric power, and possibly a semi-orthogonal complement to all those blocks. This complement is expected to be trivial by the BGMN conjecture. Our approach is based on an analysis of wall-crossing between moduli spaces of stable pairs, combining classical vector bundles techniques with the method of windows. This is joint work with Jenia Tevelev.

algebraic geometry

Audience: researchers in the topic

Derived seminar

Series comments: https://ed-ac-uk.zoom.us/j/89993982042

Password: a simply-connected two-dimensional variety with trivial canonical bundle (omit the space)