The singular locus of semisimple Hessenberg varieties
| Autor: | Erik Insko, Martha Precup |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Algebra and Number Theory 14M15 14L30 010102 general mathematics Mathematics::Rings and Algebras 01 natural sciences Mathematics::Numerical Analysis Mathematics - Algebraic Geometry Mathematics::Quantum Algebra 0103 physical sciences FOS: Mathematics 010307 mathematical physics 0101 mathematics Locus (mathematics) Mathematics::Representation Theory Algebraic Geometry (math.AG) Hessenberg variety Mathematics |
| Popis: | Although regular semisimple Hessenberg varieties are smooth and irreducible, semisimple Hessenberg varieties are not necessarily smooth in general. In this paper we determine the irreducible components of semisimple Hessenberg varieties corresponding to the standard Hessenberg space. We prove that these irreducible components are smooth and give an explicit description of their intersections, which constitute the singular locus. We conclude with an example of a semisimple Hessenberg variety corresponding to another Hessenberg space which is singular and irreducible, showing that results of this nature do not hold for all semisimple Hessenberg varieties. 24 pages, 5 figures, comments welcome |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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