### K3 surfaces of genus 17

Mukai, S *(Kyoto)*

Tuesday 12 April 2011, 15:00-16:00

Seminar Room 1, Newton Institute

#### Abstract

The moduli space M=M(2, h, 8) of semi-rigid vector bundles on a (polarized) K3 surface (S, h) of genus 17 is a K3 surface of genus 5. Moreover, the universal family gives an equivalence between the derived category of S and a twisted derived category of M. This equivalence induces us a rational map from S to the non-abelian Brill-Noether locus SU(2, K; 5F) of type II (see alg-geom/9704015) in the moduli space of 2-bundles on a curve of genus 5. We show that this map is an isomorphism when the modulus of (S, h) is general, using Thaddeus' formula. As a corollary the moduli space F17 of (S, h)’s is unirational.

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