The paper concerns the affine varieties that are homogeneous with respect to a (non-standard) graduation over the group Zm. 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 Pn.
Homogeneous varieties for Hilbert schemes
FERRARESE, Giorgio;ROGGERO, Margherita
2009-01-01
Abstract
The paper concerns the affine varieties that are homogeneous with respect to a (non-standard) graduation over the group Zm. 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 Pn.
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