Fanography

A tool to visually study the geography of Fano 3-folds.

Identification

Fano variety 2-4

blowup of 1-17 in the intersection of two cubics

Alternative description:

  • $(1,3)$-divisor on $\mathbb{P}^1\times\mathbb{P}^3$
rank
2 (others)
$-\mathrm{K}_X^3$
10
$\mathrm{h}^{1,2}(X)$
10
Hodge diamond
1
0 0
0 2 0
0 10 10 0
0 2 0
0 0
1
Anticanonical bundle
index
1
$\dim\mathrm{H}^0(X,\omega_X^\vee)$
8
$-\mathrm{K}_X$ very ample?
yes
$-\mathrm{K}_X$ basepoint free?
yes
hyperelliptic
no
trigonal
yes
Birational geometry

This variety is rational.


This variety is the blowup of

  • 1-17, in a curve of genus 10
Deformation theory
number of moduli
21

$\mathrm{Aut}^0(X)$ $\dim\mathrm{Aut}^0(X)$ number of moduli
$0$ 0 21