FanoCats

(Toric) Fano Categories Database

Smooth Fano Toric 4-folds with $\rho=3$

ID $\operatorname{rk} \mathrm{Pic}$ $\operatorname{rk} K_0$ Fan Chambers Cox degrees and $\Theta$-collection Ext table
$(4,10)$ 3 11 7: $\begin{pmatrix}-3 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & -1 & 0 \\ 0 & -1 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
14: $\begin{pmatrix}3 & 2 & 2 & 1 & 1 & 0 & 3 & 0 & -1 & 2 & -1 & -2 & 1 & 0 \\ 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0\end{pmatrix}$
$(4,11)$ 3 11 7: $\begin{pmatrix}-2 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & -1 & 0 \\ 0 & -1 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
12: $\begin{pmatrix}3 & 2 & 2 & 1 & 1 & 3 & 0 & 0 & 2 & -1 & 1 & 0 \\ 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0\end{pmatrix}$
$(4,12)$ 3 11 7: $\begin{pmatrix}-1 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 0 & 0 & -1 & 0 \\ 0 & -1 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
11: $\begin{pmatrix}3 & 2 & 2 & 3 & 1 & 1 & 2 & 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0\end{pmatrix}$
$(4,13)$ 3 12 7: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & -1 & 0 \\ 1 & 1 & 1 & 0 & 0 & -2 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
14: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 2 & 2 & 1 & 1 & 0 & -1 & 0 & -1 & 2 & 1 & 2 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$
$(4,14)$ 3 12 7: $\begin{pmatrix}1 & 1 & 1 & -2 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
15: $\begin{pmatrix}2 & 1 & 0 & -1 & 2 & 2 & 1 & 0 & 1 & -1 & 0 & -1 & 2 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$
$(4,15)$ 3 12 7: $\begin{pmatrix}1 & 1 & 1 & -1 & 0 & -1 & 0 \\ 0 & 0 & 0 & 1 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
14: $\begin{pmatrix}2 & 1 & 0 & 2 & 1 & -1 & 2 & 0 & -1 & 1 & 2 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$
$(4,16)$ 3 12 7: $\begin{pmatrix}-1 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 1 & 0 & 0 & -2 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
14: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 2 & 2 & 1 & 1 & 0 & 2 & 0 & -1 & 2 & -1 & 1 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0\end{pmatrix}$
$(4,17)$ 3 12 7: $\begin{pmatrix}1 & 1 & 1 & -2 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
14: $\begin{pmatrix}2 & 1 & 2 & 0 & 1 & 0 & 2 & -1 & -1 & 1 & 2 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0\end{pmatrix}$
$(4,18)$ 3 12 7: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & 1 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
12: $\begin{pmatrix}2 & 1 & 2 & 1 & 0 & 0 & 2 & 1 & 2 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$
$(4,19)$ 3 12 7: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 & 0 & 0 \\ -1 & 0 & 0 & 1 & 1 & 0 & 0 \\ -1 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
12: $\begin{pmatrix}2 & 2 & 2 & 2 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$
$(4,20)$ 3 12 7: $\begin{pmatrix}1 & 1 & 1 & -1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
12: $\begin{pmatrix}2 & 1 & 0 & 2 & 1 & 2 & 0 & 1 & 2 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$
$(4,21)$ 3 12 7: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 1 & -1 & 0 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
13: $\begin{pmatrix}1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 2 & 1 & 0 & 2 & 2 & 1 & 1 & -1 & 0 & 0 & 2 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0\end{pmatrix}$
$(4,22)$ 3 12 7: $\begin{pmatrix}-1 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 1 & 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
12: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 2 & 2 & 1 & 1 & 2 & 2 & 0 & 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0\end{pmatrix}$
$(4,23)$ 3 12 7: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 & 0 & 0 \\ -1 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & -1 & 0 & 1 & 1\end{pmatrix}$
12: $\begin{pmatrix}2 & 2 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 \\ 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0\end{pmatrix}$
$(4,24)$ 3 12 7: $\begin{pmatrix}1 & 1 & 1 & -1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
12: $\begin{pmatrix}2 & 1 & 2 & 0 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$
$(4,25)$ 3 12 7: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1 & 1\end{pmatrix}$
12: $\begin{pmatrix}1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 \\ 2 & 2 & 2 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$
$(4,26)$ 3 12 7: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ -1 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
12: $\begin{pmatrix}2 & 2 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$
$(4,27)$ 3 12 7: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & -1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1\end{pmatrix}$
12: $\begin{pmatrix}2 & 1 & 2 & 1 & 0 & 2 & 0 & 2 & 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0\end{pmatrix}$
$(4,28)$ 3 12 7: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 \\ 1 & 1 & 1 & -1 & 0 & 0 & -1\end{pmatrix}$
13: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ 1 & 2 & 0 & 1 & -1 & 2 & 0 & 1 & 2 & 0 & -1 & 1 & 0\end{pmatrix}$
$(4,29)$ 3 12 7: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 & 0 & 0 \\ -1 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & -1 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
12: $\begin{pmatrix}2 & 2 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 \\ 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$
$(4,30)$ 3 12 7: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 \\ 1 & 1 & 1 & 0 & 0 & 0 & -2\end{pmatrix}$
14: $\begin{pmatrix}1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ 2 & 1 & 2 & 0 & 1 & -1 & 2 & 0 & 1 & 2 & -1 & 0 & 1 & 0\end{pmatrix}$
$(4,31)$ 3 12 7: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 \\ 1 & 1 & 1 & 0 & 0 & 0 & -1\end{pmatrix}$
12: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 2 & 2 & 1 & 1 & 2 & 0 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$
$(4,32)$ 3 13 7: $\begin{pmatrix}-2 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & -1 & -1 & 0 \\ 0 & -1 & -1 & 0 & 1 & 1 & 1\end{pmatrix}$
17: $\begin{pmatrix}2 & 1 & 2 & 0 & 1 & 1 & 0 & 2 & -1 & 0 & -1 & 1 & 2 & 1 & 1 & 0 & 0 \\ 0 & 1 & -1 & 2 & 0 & -1 & 1 & 0 & 2 & 0 & 1 & 1 & -1 & 0 & -1 & 1 & 0 \\ 1 & 0 & 2 & -1 & 1 & 2 & 0 & 0 & -1 & 1 & 0 & -1 & 1 & 0 & 1 & -1 & 0\end{pmatrix}$
$(4,33)$ 3 13 7: $\begin{pmatrix}-2 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & -1 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 & 0 & -1\end{pmatrix}$
15: $\begin{pmatrix}2 & 1 & 1 & 0 & 2 & 0 & -1 & 1 & 1 & 0 & 2 & 0 & -1 & 1 & 0 \\ 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ 2 & 1 & 2 & 1 & 1 & 2 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0\end{pmatrix}$
$(4,34)$ 3 13 7: $\begin{pmatrix}-1 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & -1 & -1 & 0 \\ 0 & -1 & -1 & 0 & 1 & 1 & 1\end{pmatrix}$
15: $\begin{pmatrix}2 & 1 & 2 & 0 & 1 & 2 & 0 & 1 & 2 & 1 & 0 & 1 & 1 & 0 & 0 \\ 0 & 1 & -1 & 2 & 0 & 0 & 1 & 1 & -1 & -1 & 0 & 0 & -1 & 1 & 0 \\ 1 & 0 & 2 & -1 & 1 & 0 & 0 & -1 & 1 & 2 & 1 & 0 & 1 & -1 & 0\end{pmatrix}$
$(4,35)$ 3 13 7: $\begin{pmatrix}-1 & -1 & 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & -1 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 & 0 & -1\end{pmatrix}$
14: $\begin{pmatrix}1 & 1 & 0 & 2 & 1 & 0 & -1 & 1 & 2 & 0 & 0 & -1 & 1 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ 1 & 2 & 1 & 1 & 0 & 2 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0\end{pmatrix}$
$(4,36)$ 3 13 7: $\begin{pmatrix}1 & 0 & 0 & -1 & 0 & 0 & 1 \\ 0 & -1 & -1 & 0 & 1 & 1 & 1 \\ 0 & 1 & 1 & 1 & 0 & 0 & -1\end{pmatrix}$
14: $\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ 1 & 0 & 2 & 1 & 0 & -1 & 1 & 2 & 0 & -1 & 1 & 0 & -1 & 0 \\ 1 & 2 & 0 & 1 & 1 & 2 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0\end{pmatrix}$
$(4,37)$ 3 13 7: $\begin{pmatrix}-1 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & -1 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 & 0 & -1\end{pmatrix}$
13: $\begin{pmatrix}2 & 1 & 1 & 2 & 0 & 1 & 0 & 2 & 1 & 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 2 & 1 & 2 & 1 & 1 & 0 & 2 & 0 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$