Mukai's program (reconstructing a K3 surface from a curve) via wall-crossing

Abstract

Let $C$ be a curve of genus $g\ge 11$ such that $g-1$ is a composite number. Suppose $C$ is on a K3 surface whose Picard group is generated by the curve class $[C]$. 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 $C$ as a Fourier-Mukai transform of a Brill-Noether locus of vector bundles on $C$.

arXiv commentWe 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