## Advanced Studies in Pure Mathematics

- Adv. Stud. Pure Math.
- Minimal Models and Extremal Rays (Kyoto, 2011), J. Kollár, O. Fujino, S. Mukai and N. Nakayama, eds. (Tokyo: Mathematical Society of Japan, 2016), 379 - 396

### K3 surfaces of genus sixteen

#### 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