A free resolution of a symplectic rank variety
type: Item
instance of: scholarly article
title: A free resolution of a symplectic rank variety
zbMATH Open document ID: 0889.17020
author: J. Ning
published in: Journal of Algebra
publication date: 1998-06-11T00:00:00Z
review text: Let \(F\) be a symplectic vector space over an algebraically closed field \(K\) with characteristic different from 2. Write \(Sp(F)\) and \({\mathfrak {sp}}(F)\) for the symplectic group and its Lie algebra, respectively. Let \(Z\) be the subvariety of \({\mathfrak {sp}}(F)\) of all symplectic endomorphisms of \(F\) whose kernel contains an isotropic subspace of dimension 2. The main result of this paper uses the technique of collapsing to describe a free resolution of length 4 of the ideal of regular functions vanishing on \(Z\). In addition, the paper shows that \(Z\) is normal and has rational singularities as well as providing specific generators for the defining ideal of \(Z\).
Mathematics Subject Classification ID: 17B45
Mathematics Subject Classification ID: 14L30
zbMATH DE Number: 1088593
zbMATH Keywords: symplectic rank variety
zbMATH Keywords: free resolution
zbMATH Keywords: regular functions
zbMATH Keywords: rational singularities
reviewed by: Mark R. Sepanski
MaRDI profile type: Publication
full work available at URL: jabr.1997.7103
OpenAlex ID: W2048197793
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DOI: 10.1006/JABR.1997.7103
description: scientific article; zbMATH DE number 1088593