Fanography

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

Identification

Fano variety 2-35

$\mathrm{Bl}_p\mathbb{P}^3$

Alternative description:

  • $\mathbb{P}(\mathcal{O}_{\mathbb{P}^2}\oplus\mathcal{O}_{\mathbb{P}^2}(1))$
rank
2 (others)
$-\mathrm{K}_X^3$
56
$\mathrm{h}^{1,2}(X)$
0
Hodge diamond
1
0 0
0 2 0
0 0 0 0
0 2 0
0 0
1
Anticanonical bundle
index
2
del Pezzo of degree 7
$X\hookrightarrow\mathbb{P}^{8}$
$\dim\mathrm{H}^0(X,\omega_X^\vee)$
31
$-\mathrm{K}_X$ very ample?
yes
$-\mathrm{K}_X$ basepoint free?
yes
hyperelliptic
no
trigonal
no
Birational geometry

This variety is rational.


This variety is primitive.

This variety can be blown up (in a curve) to

  • 3-11, in a curve of genus 1
  • 3-14, in a curve of genus 1
  • 3-16, in a curve of genus 0
  • 3-19, in a curve of genus 0
  • 3-23, in a curve of genus 0
  • 3-26, in a curve of genus 0
  • 3-29, in a curve of genus 0
  • 3-30, in a curve of genus 0
Deformation theory
number of moduli
0

$\mathrm{Aut}^0(X)$ $\dim\mathrm{Aut}^0(X)$ number of moduli
$\mathrm{PGL}_{4;1}$ 12 0