Homogeneous varieties for Hilbert schemes

Abstract

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.

References added and corrected typos

References in corpus (1)

• Ideals with an assigned initial ideal

Cited by in corpus (7)

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• Double-Generic Initial Ideal and Hilbert Scheme
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• The geometry of double nested Hilbert schemes of points on curves
• The stratum of a strongly stable ideal
• Computable Hilbert Schemes
• A Borel open cover of the Hilbert scheme