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Toric variety is embedding of algebraic tori.

2 votes

Does any smooth hypersurface in (C^*)^n admit a smooth normal crossings compactifcation as a...

An obvious thing to try is to consider the Newton polytope $\Delta$ of $f$ and take $\rm Proj$ of the corresponding semigroup algebra $$ P=\rm{Proj}\oplus_{k\geq 0}\mathbb C[k\Delta]. $$ Then $Z$ is $ …
Lev Borisov's user avatar
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1 vote
Accepted

When does a discrepant toric resolution induce a crepant resolution of a subvariety?

If the subvariety $Y$ is transversal to all the strata, which is the case, for example, for generic complete intersections of base point free linear systems, then it is easy. The restriction of the r …
Lev Borisov's user avatar
  • 5,186
2 votes

What is the combinatorial data classifying non-normal affine toric varieties?

Bernd Sturmfels and others have studied varieties defined by binomial ideals. This is what you are looking for.
Lev Borisov's user avatar
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7 votes

Can one prove that toric varieties are Cohen-Macaulay by finding a regular sequence?

In my paper arXiv:math/9802052 I give an argument in the graded case. The general case can be approached similarly (as sketched in the paper). The sequence in question is made from log-derivatives of …
Lev Borisov's user avatar
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