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EFFECTIVE DIVISORS ON BOTT–SAMELSON VARIETIES

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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 ℙ1 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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Authors and Affiliations

  1. Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA

    DAVE ANDERSON

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  1. DAVE ANDERSON
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Correspondence to DAVE ANDERSON.

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The author was partially supported by NSF Grants DMS-0902967 and DMS-1502201, as well as a postdoctoral fellowship from the Instituto Nacional de Matemática Pura e Aplicada (IMPA).

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ANDERSON, D. EFFECTIVE DIVISORS ON BOTT–SAMELSON VARIETIES. Transformation Groups 24, 691–711 (2019). https://doi.org/10.1007/s00031-018-9493-6

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  • DOI: https://doi.org/10.1007/s00031-018-9493-6

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