## Advanced Studies in Pure Mathematics

### K3 surfaces of genus sixteen

Shigeru Mukai

#### Abstract

The generic polarized $K3$ surface $(S, h)$ of genus 16, that is, $(h^2)=30$, is described in a certain compactified moduli space $\mathcal T$ of twisted cubics in $\mathbb{P}^3$, as a complete intersection with respect to an almost homogeneous vector bundle of rank 10. As corollary we prove the unirationality of the moduli space $\mathcal{F}_{16}$ of such K3 surfaces.

#### Article information

Dates
Received: 29 February 2012
Revised: 28 June 2014
First available in Project Euclid: 4 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1538622713

Digital Object Identifier
doi:10.2969/aspm/07010379

Mathematical Reviews number (MathSciNet)
MR3618267

Zentralblatt MATH identifier
1369.14049

#### Citation

Mukai, Shigeru. K3 surfaces of genus sixteen. Minimal Models and Extremal Rays (Kyoto, 2011), 379--396, Mathematical Society of Japan, Tokyo, Japan, 2016. doi:10.2969/aspm/07010379. https://projecteuclid.org/euclid.aspm/1538622713