Braid and Phantom
Abstract
Let N be the moduli space of stable rank 2 vector bundles on a smooth projective curve of genus g>1 with fixed odd determinant. With Sebastian Torres, we previously found a semi-orthogonal decomposition of the bounded derived category of N into bounded derived categories of symmetric powers of the curve and, possibly, a phantom block. In this work, we employ the theory of weaving patterns to eliminate the possibility of a phantom, completing the proof of the decomposition conjectured by Narasimhan and, independently, by Belmans, Galkin, and Mukhopadhyay.
Cite
@article{arxiv.2304.01825,
title = {Braid and Phantom},
author = {Jenia Tevelev},
journal= {arXiv preprint arXiv:2304.01825},
year = {2023}
}
Comments
Due to a mistake in Lemma 3.4 in the previous version, two types of tensor vector bundles (with or without the twist by the sign representation) were treated as essentially equivalent. This error has been corrected throughout, and a new Theorem 6.14 has been added, which describes the mutation between these two types of tensor vector bundles. 45 pages