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BOTT–SAMELSON–DEMAZURE–HANSEN VARIETIES FOR PROJECTIVE HOMOGENEOUS VARIETIES WITH NONREDUCED STABILIZERS

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Abstract

Over a field of positive characteristic, a semisimple algebraic group G may have some nonreduced parabolic subgroup P. In this paper, we study the Schubert and Bott–Samelson–Demazure–Hansen (BSDH) varieties of G/P, with P nonreduced, when the base field is perfect. It is shown that, in general, the Schubert and BSDH varieties of such a G/P are not normal, and the projection of the BSDH variety onto the Schubert variety has nonreduced fibers at closed points. When the base field is finite, the generalized convolution morphisms between BSDH varieties (as in [dCHL18]) are also studied. It is shown that the decomposition theorem holds for such morphisms, and the pushforward of intersection complexes by such morphisms are Frobenius semisimple.

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  1. Department of Mathematics, Stony Brook University, Stony Brook, NY, 11794, USA

    SIQING ZHANG

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ZHANG, S. BOTT–SAMELSON–DEMAZURE–HANSEN VARIETIES FOR PROJECTIVE HOMOGENEOUS VARIETIES WITH NONREDUCED STABILIZERS. Transformation Groups 28, 1775–1800 (2023). https://doi.org/10.1007/s00031-022-09733-9

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