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Computation of the vector space T 1 for affine toric varieties

Summary: Computation of the vector space T 1 for affine
toric varieties
Klaus Altmann
Fachbereich Mathematik der Humboldt­Universit¨at zu Berlin
PSF 1297, D(O)­1086 Berlin, Germany
We compute the vector space T 1 of first order infinitesimal deformations
for affine toric varieties X oe . The result is given by two different formulas
which use combinatorial data of the given cone oe only.
One of these formulas suggests that there is a relation between deformations
of affine toric varieties on the one hand and splitting of certain polyhedra into
a Minkowski sum on the other hand.
As an application, the result is used to investigate when three­dimensional
affine toric varieties are rigid.
1 Introduction 1
2 The first T 1 ­formula for affine toric varieties 4
3 Proof of Theorem (2.3) 8
4 The second T 1 ­formula 14
5 Applications and Examples 19


Source: Altmann, Klaus - Fachbereich Mathematik und Informatik & Institut für Mathematik, Freie Universität Berlin


Collections: Mathematics