Intersection theory of the Peterson variety and certain singularities of Schubert varieties

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• 作者：Erik Insko ; Julianna Tymoczko
• 关键词：Nilpotent Hessenberg variety ; Intersection theory ; Lie algebra ; Schubert variety ; Singularity ; 14F25 ; 14C17 ; 14L30 ; 14L35
• 刊名：Geometriae Dedicata
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：180
• 期：1
• 页码：95-116
• 全文大小：725 KB
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• 作者单位：Erik Insko (1)
  Julianna Tymoczko (2)
  
  1. Department of Mathematics, Florida Gulf Coast University, Ft Myers, FL, 33965, USA
  2. Department of Mathematics, Smith College, Northampton, MA, 01063, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Geometry
  
• 出版者：Springer Netherlands
• ISSN：1572-9168

文摘

Precup recently proved that intersections with Schubert cells pave regular nilpotent Hessenberg varieties. We use this paving to prove that the homology of the Peterson variety injects into the homology of the full flag variety. The proof uses intersection theory and expands the class of the Peterson variety in the homology of the flag variety in terms of the basis of Schubert classes. We explicitly identify some of the coefficients of Schubert classes in this expansion, answering a problem of independent interest in Schubert calculus. We also identify some singular points in a certain family of Schubert varieties in general Lie type. Keywords Nilpotent Hessenberg variety Intersection theory Lie algebra Schubert variety Singularity