Mukai's program (reconstructing a K3 surface from a curve) via wall-crossing
Algebraic Geometry
2020-06-17 v2
Abstract
Let be a curve of genus such that is a composite number. Suppose is on a K3 surface whose Picard group is generated by the curve class . We use wall-crossing with respect to Bridgeland stability conditions to generalise Mukai's program to this situation: we show how to reconstruct the K3 surface containing the curve as a Fourier-Mukai transform of a Brill-Noether locus of vector bundles on .
Cite
@article{arxiv.1710.06692,
title = {Mukai's program (reconstructing a K3 surface from a curve) via wall-crossing},
author = {Soheyla Feyzbakhsh},
journal= {arXiv preprint arXiv:1710.06692},
year = {2020}
}
Comments
We explain why the published version of this paper [DOI: 10.1515/crelle-2019-0025] is only valid for g-1 a composite number. The new paper arXiv:2006.08410 handles the remaining case that g-1 is prime