The subregular variety to the variety of special lattices
type: Item
instance of: scholarly article
title: The subregular variety to the variety of special lattices
zbMATH Open document ID: 1208.14040
author: Akira Sano
published in: Journal of Pure and Applied Algebra
publication date: 2011-01-07T00:00:00Z
review text: Let \(k\) be the algebraic closure of a finite field of characteristic \(p\) and let \(\mathcal{O}\) be the \(k\)-points of the Witt vectors and \(K\) the fraction field of \(\mathcal{O}\). Let \(F=\mathcal{O}^n\subset K^n\) be the standard inclusion. A lattice \(L\) as usual will be a free \(\mathcal{O}\)-submodule of rank \(n\) of \(K^n\). It is called special if \(\bigwedge^n L=\bigwedge^n F\) and it is of height at most \(r>0\) if \(L\subset p^{-r}F\). \textit{W. J. Haboush} proved that the set of all special lattices (fixing \(n,r\)) form a projective variety [Tohoku Math. J. (2) 57, No. 1, 65--117 (2005; Zbl 1119.14004)]. In the author's thesis, he proved that these are normal and the author and Haboush proved that these are local complete intersections. In the present article, the author shows that the singular locus of the lattice variety is also normal and local complete intersection.
reviewed by: N. Mohan Kumar
Mathematics Subject Classification ID: 14M15
Mathematics Subject Classification ID: 20G25
Mathematics Subject Classification ID: 20G99
zbMATH DE Number: 5833923
zbMATH Keywords: Witt vectors
zbMATH Keywords: lattices
zbMATH Keywords: normal variety
zbMATH Keywords: local complete intersection variety
MaRDI profile type: Publication
full work available at URL: j.jpaa.2010.06.007
OpenAlex ID: W2027209590
cites work: Q4099737
cites work: Q3999894
cites work: Line bundles on the cotangent bundle of the flag variety
cites work: Algebraic loop groups and moduli spaces of bundles
cites work: Q4422482
cites work: Infinite dimensional algebraic geometry: algebraic structures on \(p\)-adic groups and their homogeneous spaces
cites work: Frobenius splitting of cotangent bundles of flag varieties
cites work: Closures of conjugacy classes of matrices are normal
cites work: Green polynomials and singularities of unipotent classes
cites work: Q3992979
cites work: Q4740026
cites work: Local models in the ramified case. I: The EL-case
cites work: Another proof of a theorem on rational cross sections
DOI: 10.1016/J.JPAA.2010.06.007
description: scientific article; zbMATH DE number 5833923