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

Abstract

We show that the Poincaré bundle gives a fully faithful embedding 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. Moreover we show that a twist of the embedding, together with 2 exceptional line bundles, gives the start of a semi-orthogonal decomposition. This generalises results of Narasimhan and Fonarev-Kuznetsov, who embedded the derived category of a single copy of the curve, for rank 2.

arXiv comment17 pages

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Cited by in corpus (6)

• Derived categories of (nested) Hilbert schemes
• Derived categories of flips and cubic hypersurfaces
• Decompositions of moduli spaces of vector bundles and graph potentials
• Polyvector fields for Fano 3-folds
• Vector fields and admissible embeddings for quiver moduli
• Smooth components on special iterated Hilbert schemes