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

Pieter Belmans; Swarnava Mukhopadhyay

doi:10.1007/s00029-019-0482-y

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arXiv · 1807.00216

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

Pieter Belmans·Swarnava Mukhopadhyay

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Abstract

We show that the Poincar\'e 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.

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BibTeX RIS

Pieter Belmans, Swarnava Mukhopadhyay. 2018-06-30. Admissible subcategories in derived categories of moduli of vector bundles on curves. https://doi.org/10.1007/s00029-019-0482-y

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