On the singularity of some special components of Springer fibers - Mathematics > Algebraic GeometryReportar como inadecuado




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Abstract: Let $u\in\mathrm{End}\mathbb{C}^n$ be nilpotent. The variety of $u$-stablecomplete flags is called the Springer fiber over $u$. Its irreduciblecomponents are parameterized by a set of standard Young tableaux. TheRichardson resp. Bala-Carter components of Springer fibers correspond to theRichardson resp. Bala-Carter elements of the symmetric group, throughRobinson-Schensted correspondence. Every Richardson component is isomorphic toa product of standard flag varieties. On the contrary, the Bala-Cartercomponents are very susceptible to be singular. First, we characterize thesingular Bala-Carter components in terms of two minimal forbiddenconfigurations. Next, we introduce two new families of components, wider thanthe families of Bala-Carter components and Richardson components, and both induality via the tableau transposition. The components in the first family arecharacterized by the fact that they have a dense orbit of special type underthe action of the stabilizer of $u$, whereas all components in the secondfamily are iterated fiber bundles over projective spaces.



Autor: Lucas Fresse

Fuente: https://arxiv.org/



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