Combinatorial invariance of toric singularities
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (1982), pp. 80-87
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The are two theorems in this paper.
1. Let $\sigma_1$ and $\sigma_2$ be convex polyhedral cones in an $n$-dimensional lattice. Let $X_1$, $X_2$ be their associated affine toric varieties. $X_1$ and $X_2$ are isomorphic iff $\sigma_1$ and $\sigma_2$ are isomorphic.
2. Let $X_1$, $X_2$ be affine toric varieties. Let $T_1$ be a torus, embedded in $X_1$, $T_2$ be the same tor $X_2$. $X_1$, $X_2$ are isomorphic iff there exists a formal isomorphism between the points of maximal strati on $X_1$, $X_2$.
@article{VMUMM_1982_2_a18,
author = {A. S. Demushkin},
title = {Combinatorial invariance of toric singularities},
journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
pages = {80--87},
publisher = {mathdoc},
number = {2},
year = {1982},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMUMM_1982_2_a18/}
}
A. S. Demushkin. Combinatorial invariance of toric singularities. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (1982), pp. 80-87. http://geodesic.mathdoc.fr/item/VMUMM_1982_2_a18/