Cohomology Rings and Algebraic Torus Actions on Hypersurfaces in the Product of Projective Spaces and Bounded Flag Varieties

被引：0
作者：
Solomadin G. [1 ]
机构：
[1] International Laboratory of Algebraic Topology and its Applications, Faculty of Computer Science, Higher School of Economics, Moscow
来源：
Arnold Mathematical Journal | 2023年 / 9卷 / 1期
基金：
俄罗斯基础研究基金会;
关键词：
Automorphisms of algebraic varieties; Blow-ups; Fiber bundles; Hypergraphs; Toric varieties; Torus actions;
D O I：
10.1007/s40598-022-00203-4
中图分类号：
学科分类号：
摘要：
In this paper, for any Milnor hypersurface, we find the largest dimension of effective algebraic torus actions on it. The proof of the corresponding theorem is based on the computation of the automorphism group for any Milnor hypersurface. We find all generalized Buchstaber–Ray and Ray hypersurfaces that are toric varieties. We compute the Betti numbers of these hypersurfaces and describe their integral singular cohomology rings in terms of the cohomology of the corresponding ambient varieties. © 2022, Institute for Mathematical Sciences (IMS), Stony Brook University, NY.
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页码：105 / 150
页数：45
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