论文标题
Bott-Samelson-Demazure-Hansen品种用于未还原稳定器的投影均匀品种
Bott-Samelson-Demazure-Hansen Varieties for Projective Homogeneous Varieties with Nonreduced Stabilizers
论文作者
论文摘要
在一个积极特征的领域，半代数组$ g $可能具有一些未还原的抛物线亚组$ p $。在本文中，我们研究了$ g/p $的Schubert和Bott-Samelson-Demazure-Hansen（BSDH）品种，当基本场是完美的时候，$ p $ nonducces。 结果表明，这种$ g/p $的Schubert和BSDH品种不正常，而BSDH品种在Schubert品种上的投影在封闭点上没有还原纤维。 当基地是有限的时，还研究了BSDH品种之间的广义卷积形态。结果表明，分解定理对这种形态性存在，这种形态的相交复合物的推动是Frobenius Semisimple。
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 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.
