Mukai's Program (reconstructing a K3 surface from a curve) via wall-crossing, II

TL;DR

This paper advances Mukai's program by employing wall-crossing techniques in Bridgeland stability to reconstruct a K3 surface from a curve, specifically addressing the case where the genus minus one is prime.

Contribution

It extends previous work by proving the reconstruction for genus g-1 prime cases using wall-crossing in Bridgeland stability conditions.

Findings

Reconstruction of K3 surfaces from curves with genus ≥14.

Application of wall-crossing techniques in Bridgeland stability.

Resolution of the prime genus g-1 case from prior research.

Abstract

Let $C$ be a curve on a K3 surface $X$ with Picard group $\mathbb{Z}.[C]$. Mukai's program seeks to recover $X$ from $C$ by exhibiting it as a Fourier-Mukai partner to a Brill-Noether locus of vector bundles on $C$. We use wall-crossing in the space of Bridgeland stability conditions to prove this for genus $\ge14$. This paper deals with the case $g-1$ prime left over from Paper I.