Combinatorial Models for the Variety of Complete Quadrics

Soumya Banerjee; Mahir Bilen Can; Michael Joyce

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arXiv · 1610.02698

Combinatorial Models for the Variety of Complete Quadrics

Soumya Banerjee·Mahir Bilen Can·Michael Joyce

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Abstract

We develop several combinatorial models that are useful in the study of the $SL_n$-variety $\mathcal{X}$ of complete quadrics. Barred permutations parameterize the fixed points of the action of a maximal torus $T$ of $SL_n$, while $\mu$-involutions parameterize the orbits of a Borel subgroup of $SL_n$. Using these combinatorial objects, we characterize the $T$-stable curves and surfaces on $\mathcal{X}$, compute the $T$-equivariant $K$-theory of $\mathcal{X}$, and describe a Bia{\l}ynicki-Birula cell decomposition for $\mathcal{X}$. Furthermore, we give a computational characterization of the Bruhat order on Borel orbits in $\mathcal{X}$.

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BibTeX RIS

Soumya Banerjee, Mahir Bilen Can, Michael Joyce. 2016-10-09. Combinatorial Models for the Variety of Complete Quadrics. https://arxiv.org/abs/1610.02698

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