The cohomology rings of smooth toric varieties and quotients of moment-angle complexes

IF 2 1区 数学
M. Franz
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引用次数: 17

Abstract

Partial quotients of moment-angle complexes are topological analogues of smooth, not necessarily compact toric varieties. In 1998, Buchstaber and Panov proposed a formula for the cohomology ring of such a partial quotient in terms of a torsion product involving the corresponding Stanley-Reisner ring. We show that their formula gives the correct cup product if 2 is invertible in the chosen coefficient ring, but not in general. We rectify this by defining an explicit deformation of the canonical multiplication on the torsion product.
光滑环型的上同环和矩角配合物的商
矩角配合物的部分商是光滑的拓扑类似物,不一定是紧致环的变种。Buchstaber和Panov在1998年用涉及相应Stanley-Reisner环的扭转积提出了这种偏商的上同环的公式。我们证明,如果2在所选系数环中可逆,则他们的公式给出了正确的杯积,但一般情况下不是这样。我们通过定义扭积上正则乘法的显式变形来纠正这一点。
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来源期刊
Geometry & Topology
Geometry & Topology 数学-数学
自引率
5.00%
发文量
34
期刊介绍: Geometry and Topology is a fully refereed journal covering all of geometry and topology, broadly understood. G&T is published in electronic and print formats by Mathematical Sciences Publishers. The purpose of Geometry & Topology is the advancement of mathematics. Editors evaluate submitted papers strictly on the basis of scientific merit, without regard to authors" nationality, country of residence, institutional affiliation, sex, ethnic origin, or political views.
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