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arXiv · 1501.00034

Effective divisors on Bott-Samelson varieties

Dave Anderson
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Abstract

We compute the cone of effective divisors on a Bott-Samelson variety corresponding to an arbitrary sequence of simple roots. The main tool is a general result concerning effective cones of certain $B$-equivariant $\mathbb{P}^1$ bundles. As an application, we compute the cone of effective codimension-two cycles on Bott-Samelson varieties corresponding to reduced words. We also obtain an auxiliary result giving criteria for a Bott-Samelson variety to contain a dense $B$-orbit, and we construct desingularizations of intersections of Schubert varieties. An appendix exhibits an explicit divisor showing that any Bott-Samelson variety is log Fano.

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Dave Anderson. 2018-01-20. Effective divisors on Bott-Samelson varieties. https://arxiv.org/abs/1501.00034

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