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On the equations defining some Hilbert schemes

Abstract:
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.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s10013-021-00545-0

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
St Peter's College
Role:
Author
ORCID:
0000-0002-0092-4719


Publisher:
Springer
Journal:
Vietnam Journal of Mathematics More from this journal
Volume:
50
Issue:
2
Pages:
487–500
Publication date:
2022-01-22
Acceptance date:
2021-11-19
DOI:
EISSN:
2305-2228
ISSN:
2305-221X


Language:
English
Keywords:
Pubs id:
1170011
Local pid:
pubs:1170011
Deposit date:
2021-11-26

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