Identification

Hodge diamond

1

0 0

0 2 0

0 6 6 0

0 2 0

0 0

1

0 0

0 2 0

0 6 6 0

0 2 0

0 0

1

Anticanonical bundle

- index
- 1
- $\dim\mathrm{H}^0(X,\omega_X^\vee)$
- 9
- $-\mathrm{K}_X$ very ample?
- yes
- $-\mathrm{K}_X$ basepoint free?
- yes
- hyperelliptic
- no
- trigonal
- yes

Birational geometry

This variety is not rational but unirational.

This variety is the blowup of

- 1-13, in a curve of genus 1

Deformation theory

- number of moduli
- 16

$\mathrm{Aut}^0(X)$ | $\dim\mathrm{Aut}^0(X)$ | number of moduli |
---|---|---|

$0$ | 0 | 16 |