Admissible subcategories in derived categories of moduli of vector bundles on curves

Abstract

We show that the Poincaré bundle gives a fully faithful functor from the derived category of a curve of sufficiently high genus into the derived category of its moduli space of bundles of rank r with fixed determinant of degree 1. This generalises results of Narasimhan and Fonarev–Kuznetsov for the case of rank 2, and also gives an alternative proof of known results on deformations of universal bundles. Moreover we show that a twist of the embedding, together with 2 exceptional line bundles, gives the beginning of a semiorthogonal decomposition for the derived category of the moduli space.