Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-03T02:28:14.852Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
JANUSZ GRABOWSKI
Affiliation:
Instytut Matematyki, Uniwersytet Warszawski, PL 02-097 Warsaw, Poland; e-mail: [email protected]
GERD MÜLLER
Affiliation:
Fachbereich Mathematik, Universität Mainz, D55099 Mainz, Germany e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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