Fanography

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

Identification

Fano variety 2-1

blowup of 1-11 in an elliptic curve which is the intersection of two divisors from half the anticanonical linear system

rank
2 (others)
$-\mathrm{K}_X^3$
4
$\mathrm{h}^{1,2}(X)$
22
Hodge diamond
1
0 0
0 2 0
0 22 22 0
0 2 0
0 0
1
Anticanonical bundle
index
1
$\dim\mathrm{H}^0(X,\omega_X^\vee)$
5
$-\mathrm{K}_X$ very ample?
no
$-\mathrm{K}_X$ basepoint free?
no
hyperelliptic
no
trigonal
no
Birational geometry

This variety is not known to be unirational.


This variety is the blowup of

  • 1-11, in a curve of genus 1
Deformation theory
number of moduli
26

$\mathrm{Aut}^0(X)$ $\dim\mathrm{Aut}^0(X)$ number of moduli
$0$ 0 26