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

Soheyla Feyzbakhsh

Published 2017-10-18Version 1

Let $C$ be a curve of genus $g=11$ or $g \geq 13$ 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 $C$.