FanoCats

(Toric) Fano Categories Database

Smooth Fano Toric 4-folds with $\rho\leq2$

ID $\operatorname{rk} \mathrm{Pic}$ $\operatorname{rk} K_0$ Fan Chambers Cox degrees and $\Theta$-collection Ext table
$(4,0)$ 1 5 5: $\begin{pmatrix}1 & 1 & 1 & 1 & 1\end{pmatrix}$
5: $\begin{pmatrix}4 & 3 & 2 & 1 & 0\end{pmatrix}$
$(4,1)$ 2 8 6: $\begin{pmatrix}1 & 1 & 1 & 1 & -3 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
10: $\begin{pmatrix}3 & 2 & 1 & 0 & 3 & -1 & -2 & 2 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0\end{pmatrix}$
$(4,2)$ 2 8 6: $\begin{pmatrix}1 & 1 & 1 & 1 & -2 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
9: $\begin{pmatrix}3 & 2 & 1 & 0 & 3 & -1 & 2 & 1 & 0 \\ 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0\end{pmatrix}$
$(4,3)$ 2 8 6: $\begin{pmatrix}1 & 1 & 1 & 1 & -1 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
8: $\begin{pmatrix}3 & 2 & 1 & 3 & 0 & 2 & 1 & 0 \\ 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0\end{pmatrix}$
$(4,4)$ 2 8 6: $\begin{pmatrix}1 & 1 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
8: $\begin{pmatrix}3 & 2 & 3 & 1 & 2 & 0 & 1 & 0 \\ 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0\end{pmatrix}$
$(4,5)$ 2 8 6: $\begin{pmatrix}1 & 1 & 1 & 1 & 0 & 0 \\ -1 & 0 & 0 & 0 & 1 & 1\end{pmatrix}$
8: $\begin{pmatrix}3 & 3 & 2 & 2 & 1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0\end{pmatrix}$
$(4,6)$ 2 9 6: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 & 0 \\ -2 & 0 & 0 & 1 & 1 & 1\end{pmatrix}$
11: $\begin{pmatrix}2 & 2 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 0 \\ 2 & 1 & 0 & 2 & -1 & 1 & 0 & 2 & -1 & 1 & 0\end{pmatrix}$
$(4,7)$ 2 9 6: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 & 0 \\ -1 & 0 & 0 & 1 & 1 & 1\end{pmatrix}$
9: $\begin{pmatrix}2 & 2 & 1 & 2 & 1 & 0 & 1 & 0 & 0 \\ 2 & 1 & 2 & 0 & 1 & 2 & 0 & 1 & 0\end{pmatrix}$
$(4,8)$ 2 9 6: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 & 0 \\ -1 & -1 & 0 & 1 & 1 & 1\end{pmatrix}$
10: $\begin{pmatrix}2 & 1 & 2 & 1 & 2 & 0 & 1 & 0 & 1 & 0 \\ 1 & 2 & 0 & 1 & -1 & 2 & 0 & 1 & -1 & 0\end{pmatrix}$
$(4,9)$ 2 9 6: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1\end{pmatrix}$
9: $\begin{pmatrix}2 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 0 \\ 2 & 2 & 1 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$