# Fanography

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

## Fano threefolds with $\rho=4$

ID $-\mathrm{K}_X^3$ $\mathrm{h}^{1,2}$ description
4-1 24 1

divisor on $\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^1$ of degree $(1,1,1,1)$

4-2 28 1

blowup of the cone over a smooth quadric in $\mathbb{P}^3$ in the disjoint union of the vertex and an elliptic curve on the quadric

4-3 30 0

blowup of 3-27 in a curve of degree $(1,1,2)$

4-4 32 0

blowup of 3-19 in the proper transform of a conic through the points

4-5 32 0

blowup of 2-34 in the disjoint union of a curve of degree $(2,1)$ and a curve of degree $(1,0)$

4-6 34 0

blowup of 1-17 in the disjoint union of 3 lines

4-7 36 0

blowup of 2-32 in the disjoint union of a curve of degree $(0,1)$ and a curve of degree $(1,0)$

4-8 38 0

blowup of 3-27 in a curve of degree $(0,1,1)$

4-9 40 0

blowup of 3-25 in an exceptional curve of the blowup

4-10 42 0

$\mathbb{P}^1\times\mathrm{Bl}_2\mathbb{P}^2$

4-11 44 0

blowup of 3-28 in $\{x\}\times E$, $x\in\mathbb{P}^1$ and $E$ the $(-1)$-curve

4-12 46 0

blowup of 2-33 in the disjoint union of two exceptional lines of the blowup

4-13 26 0

blowup of 3-27 in a curve of degree $(1,1,3)$