Journal article
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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- Files:
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(Preview, Accepted manuscript, pdf, 323.8KB, Terms of use)
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- Publisher copy:
- 10.1007/s10013-021-00545-0
Authors
- 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:
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2305-2228
- ISSN:
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2305-221X
Terms of use
- Copyright holder:
- Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd
- Copyright date:
- 2021
- Rights statement:
- © Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2022
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from Springer at: https://doi.org/10.1007/s10013-021-00545-0
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