Fanography

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

Fano threefolds with $\rho=5$

ID $-\mathrm{K}_X^3$ $\mathrm{h}^{1,2}$ description blowups blowdowns rational unirational moduli $\mathrm{Aut}^0$
5-1 28 0

blowup of 2-29 in the disjoint union of three exceptional lines of the blowup

4-4, 4-12 yes yes 0 $\mathbb{G}_{\mathrm{m}}$
5-2 36 0

blowup of 3-25 in the disjoint union of two exceptional lines on the same irreducible component

4-9, 4-11, 4-12 yes yes 0 $\mathbb{G}_{\mathrm{m}}\times\mathrm{GL}_2$
5-3 36 0

$\mathbb{P}^1\times\mathrm{Bl}_3\mathbb{P}^2$

* 4-10 yes yes 0 $\mathrm{PGL}_2\times\mathbb{G}_{\mathrm{m}}^2$