Fanography

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

Identification

Fano variety 2-15
  1. blowup of 1-17 in the intersection of a quadric and a cubic where the quadric is smooth
  2. blowup of 1-17 in the intersection of a quadric and a cubic where the quadric is singular but reduced
rank
2 (others)
$-\mathrm{K}_X^3$
22
$\mathrm{h}^{1,2}(X)$
4
Hodge diamond
1
0 0
0 2 0
0 4 4 0
0 2 0
0 0
1
Anticanonical bundle
index
1
$\dim\mathrm{H}^0(X,\omega_X^\vee)$
14
$-\mathrm{K}_X$ very ample?
yes
$-\mathrm{K}_X$ basepoint free?
yes
hyperelliptic
no
trigonal
no
Birational geometry

This variety is rational.


This variety is the blowup of

  • 1-17, in a curve of genus 4
Deformation theory
number of moduli
  1. 9
  2. 8

$\mathrm{Aut}^0(X)$ $\dim\mathrm{Aut}^0(X)$ number of moduli
$0$ 0 9