Stable reductive varieties I: Affine varieties

Details Stable reductive varieties I: Affine varieties Stable reductive varieties I: Affine varieties

2002-07-29

arxiv.org/abs/math/0207272v2

Mathematics

Algebraic Geometry

47 pages

Scientific paper

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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