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Research Article | Open Access

Additive actions on hyperquadrics of corank two

Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
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Abstract

For a projective variety X in Pm of dimension n, an additive action on X is an effective action of Gan on Pm such that X is Gan-invariant and the induced action on X has an open orbit. Arzhantsev and Popovskiy have classified additive actions on hyperquadrics of corank 0 or 1. In this paper, we give the classification of additive actions on hyperquadrics of corank 2 whose singularities are not fixed by the Gan-action.

Keywords

commutative unipotent group actionequivariant compactificationhyperquadric of corank twosymmetric bilinear formsimultaneous orthogonal similarity

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Electronic Research Archive
Volume 30 Issue 1,
January 2022
Pages 1-34
DOI: 10.3934/era.2022001

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Cite this article:
Liu Y. Additive actions on hyperquadrics of corank two. Electronic Research Archive, 2022, 30(1): 1-34. https://doi.org/10.3934/era.2022001

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Received: 24 March 2021
Revised: 30 September 2021
Accepted: 12 October 2021
Published: 15 January 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)