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Article Dans Une Revue Vietnam Journal of Mathematics Année : 2022

On the equations defining some Hilbert schemes

Résumé

We work out details of the extrinsic geometry for two Hilbert schemes of some contemporary interest: the Hilbert scheme of two points on the projective plane and the dense open set parametrizing non-planar clusters in the punctual Hilbert scheme of clusters of length four on affine three-space with support at the origin. We find explicit equations in natural projective, respectively affine embeddings for these spaces. In particular, we answer a question of Bernd Sturmfels who asked for a description of the latter space that is amenable to further computations. While the explicit equations we find are controlled in a precise way by the representation theory of SL_3, our arguments also rely on computer algebra.

Dates et versions

hal-03514369 , version 1 (06-01-2022)

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Jonathan D. Hauenstein, Laurent Manivel, Balazs Szendroi. On the equations defining some Hilbert schemes. Vietnam Journal of Mathematics, 2022, 50, pp.487-500. ⟨hal-03514369⟩
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