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Derivation Algebras of Toric Varieties

Published online by Cambridge University Press:  04 December 2007

ANTONIO CAMPILLO ,
JANUSZ GRABOWSKI  and
GERD MÜLLER
ANTONIO CAMPILLO
Affiliation:
Departamento de Algebra, Geometria y Topologia, Universidad de Valladolid, E 47005 Valladolid, Spain. e-mail: campillo@cpd.uva.es
JANUSZ GRABOWSKI
Affiliation:
Instytut Matematyki, Uniwersytet Warszawski, PL 02-097 Warsaw, Poland; e-mail: jagrab@mimuw.edu.pl
GERD MÜLLER
Affiliation:
Fachbereich Mathematik, Universität Mainz, D55099 Mainz, Germany e-mail: mueller@mat.mathematik.uni-maiz.de
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Abstract

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We study the Lie algebra of derivations of the coordinate ring of affine toric varieties defined by simplicial affine semigroups and prove the following results:

Such toric varieties are uniquely determined by their Lie algebra if they are supposed to be Cohen–Macaulay of dimension [ges ] 2 or Gorenstein of dimension =1.

In the Cohen–Macaulay case, every automorphism of the Lie algebra is induced from a unique automorphism of the variety.

Every derivation of the Lie algebra is inner.

Keywords

toric varietyaffine semigroupderivationLie algebraroot space decomposition.
Type
Research Article
Information
Compositio Mathematica , Volume 116 , Issue 2 , April 1999 , pp. 119 - 132
Copyright
© 1999 Kluwer Academic Publishers