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- Title
Stable reductive varieties I: Affine varieties.
- Authors
Alexeev, Valery; Brion, Michel
- Abstract
This article studies stable reductive varieties. The main motivation for this work is to extend the construction of the moduli spaces of polarized abelian varieties Ag and their compactifications to a non-commutative setting. An interesting consequence of the classification is the toric correspondence: it turns out that stable reductive varieties are in bijection with stable toric varieties equipped with a compatible W-action. Another nice feature of reductive varieties is the existence of an associative multiplication law, making each of them into an algebraic semigroup.
- Subjects
TOPOLOGY; SET theory; CLASSIFICATION; VARIETIES (Universal algebra); CONGRUENCE modular varieties; MATHEMATICS
- Publication
Inventiones Mathematicae, 2004, Vol 157, Issue 2, p227
- ISSN
0020-9910
- Publication type
Article
- DOI
10.1007/s00222-003-0347-y