Variety information
Id
270
Rays
\(\begin{bmatrix}
-1 \\ -1 \\ 0
\end{bmatrix}\)
,\(\begin{bmatrix}
1 \\ 0 \\ 0
\end{bmatrix}\)
,\(\begin{bmatrix}
0 \\ 1 \\ 0
\end{bmatrix}\)
,\(\begin{bmatrix}
0 \\ 0 \\ 1
\end{bmatrix}\)
,\(\begin{bmatrix}
18 \\ 20 \\ -1
\end{bmatrix}\)
Max cones
\(\begin{bmatrix}
0 \\ 1 \\ 3
\end{bmatrix}\)
,\(\begin{bmatrix}
0 \\ 1 \\ 4
\end{bmatrix}\)
,\(\begin{bmatrix}
0 \\ 2 \\ 3
\end{bmatrix}\)
,\(\begin{bmatrix}
0 \\ 2 \\ 4
\end{bmatrix}\)
,\(\begin{bmatrix}
1 \\ 2 \\ 3
\end{bmatrix}\)
,\(\begin{bmatrix}
1 \\ 2 \\ 4
\end{bmatrix}\)
Weil to class group
\(\begin{bmatrix}
0 & -18 & -20 & 1 & 1 \\ 1 & 1 & 1 & 0 & 0
\end{bmatrix}\)
Dimension
3
Picard rank
2
Tags
kleinschmidt
Description
kleinschmidt variety \(X_3(18,20)\)
Metadata
| Key | Value |
|---|---|
| macaulay2_code | kleinschmidt(3, {18,20}) |