 
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
Abstract
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.
Contents
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
