singularities-richardson-7 (1).pdf (321.9 kB)
Singularities of Generalized Richardson Varieties
journal contribution
posted on 2013-11-15, 00:00 authored by Sara Billey, Izzet CoskunRichardson varieties play an important role in intersection theory and in the geometric
interpretation of the Littlewood-Richardson Rule for
ag varieties. We discuss three natural generalizations
of Richardson varieties which we call projection varieties, intersection varieties, and rank varieties.
In many ways, these varieties are more fundamental than Richardson varieties and are more easily
amenable to inductive geometric constructions. In this paper, we study the singularities of each type
of generalization. Like Richardson varieties, projection varieties are normal with rational singularities.
We also study in detail the singular loci of projection varieties in Type A Grassmannians. We use
Kleiman's Transversality Theorem to determine the singular locus of any intersection variety in terms of
the singular loci of Schubert varieties. This is a generalization of a criterion for any Richardson variety
to be smooth in terms of the nonvanishing of certain cohomology classes which has been known by some
experts in the eld, but we don't believe has been published previously.
Funding
National Science Foundation (NSF) grant DMS-0800978. NSF grant DMS-0737581, NSF CAREER grant DMS-0950951535 and an Alfred P. Sloan Foundation Fellowship
History
Publisher Statement
Post print version of article may differ from published version. This is an electronic version of an article published in Billey, S. and I. Coskun (2012). "Singularities of Generalized Richardson Varieties." Communications in Algebra 40(4): 1466-1495.DOI: 10.1080/00927872.2011.551903. Communications in Algebra is available online at: http://www.informaworld.com/smpp/ DOI: 10.1080/00927872.2011.551903Publisher
Taylor and FrancisLanguage
- en_US
issn
0092-7872Issue date
2012-04-01Usage metrics
Categories
No categories selectedKeywords
Licence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC