Homogeneous varieties for Hilbert schemes

Details Homogeneous varieties for Hilbert schemes Homogeneous varieties for Hilbert schemes

2009-01-21

arxiv.org/abs/0901.3263v2

Mathematics

Commutative Algebra

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Scientific paper

The paper concerns the affine varieties that are homogeneous with respect to a (non-standard) graduation over the group Z^m. Among the other properties it is shown that every such a variety can be embedded in its Zariski tangent space at the origin, so that it is smooth if and only if it is isomorphic to an affine space. The results directly apply to the study of Hilbert schemes of subvarieties in P^n.

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