# Fanography

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

## Fano threefolds with $\rho=1$

ID $-\mathrm{K}_X^3$ $\mathrm{h}^{1,2}$ index description
1-1 2 52 1

double cover of $\mathbb{P}^3$ with branch locus a divisor of degree 6

1-2 4 30 1
1. hypersurface of degree 4 in $\mathbb{P}^4$
2. double cover of 1-16 with branch locus a divisor of degree 8
1-3 6 20 1

complete intersection of quadric and cubic in $\mathbb{P}^5$

1-4 8 14 1

complete intersection of 3 quadrics in $\mathbb{P}^6$

1-5 10 10 1 Gushel–Mukai 3-fold
1. section of Plücker embedding of $\mathrm{Gr}(2,5)$ by codimension 2 subspace and a quadric
2. double cover of 1-15 with branch locus an anticanonical divisor
1-6 12 7 1

section of half-spinor embedding of a connected component of $\mathrm{OGr}_+(5,10)$ by codimension 7 subspace

1-7 14 5 1

section of Plücker embedding of $\mathrm{Gr}(2,6)$ by codimension 5 subspace

1-8 16 3 1

section of Plücker embedding of $\mathrm{SGr}(3,6)$ by codimension 3 subspace

1-9 18 2 1

section of the adjoint $\mathrm{G}_2$-Grassmannian $\mathrm{G}_2\mathrm{Gr}(2,7)$ by codimension 2 subspace

1-10 22 0 1

zero locus of $(\bigwedge^2\mathcal{U}^\vee)^{\oplus 3}$ on $\mathrm{Gr}(3,7)$

1-11 8 21 2

hypersurface of degree 6 in $\mathbb{P}(1,1,1,2,3)$

1-12 16 10 2

double cover of $\mathbb{P}^3$ with branch locus a smooth quartic surface

1-13 24 5 2

hypersurface of degree 3 in $\mathbb{P}^4$

1-14 32 2 2

complete intersection of 2 quadrics in $\mathbb{P}^5$

1-15 40 0 2

section of Plücker embedding of $\mathrm{Gr}(2,5)$ by codimension 3 subspace

1-16 54 0 3

hypersurface of degree 2 in $\mathbb{P}^4$

1-17 64 0 4

projective space $\mathbb{P}^3$