Stable reductive varieties I: Affine varieties

Valery Alexeev; Michel Brion

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Stable reductive varieties I: Affine varieties

Valery Alexeev·Michel Brion

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Abstract

The motivation of this work is to construct an analog of compactified moduli of abelian varieties and toric pairs in the case of non-commutative algebraic group G. We introduce a class of "stable reductive varieties" which contain connected reductive groups and their equivariant compactifications, and is closed under flat reduced degenerations. We classify them all, describe their degenerations, and establish a connection between these varieties and "reductive semigroups" which we also define. Finally, we construct a Hilbert scheme of embedded G-varieties by applying and generalizing a construction of Haiman and Sturmfels. The second version adds some cosmetic changes.

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BibTeX RIS

Valery Alexeev, Michel Brion. 2003-09-15. Stable reductive varieties I: Affine varieties. https://arxiv.org/abs/math/0207272

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