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The Cohomology Groups of Real Toric Varieties Associated with Weyl Chambers of Types C and D

Part of: Lie algebras and Lie superalgebras Special varieties Topological manifolds

Published online by Cambridge University Press:  14 February 2019

Suyoung Choi ,
Shizuo Kaji  and
Hanchul Park
Suyoung Choi
Affiliation:
Department of Mathematics, Ajou University, 206, World Cup-ro, Yeongtong-gu, Suwon 16499, Republic of Korea (schoi@ajou.ac.kr)
Shizuo Kaji
Affiliation:
Institute of Mathematics for Industry, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan (skaji@imi.kyushu-u.ac.jp)
Hanchul Park
Affiliation:
Department of Mathematics Education, Jeju National University, 102 Jejudaehak-ro, Jeju-si, Jeju Province, 63243, Republic of Korea (hanchulp@jejunu.ac.kr)
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Abstract

Given a root system, the Weyl chambers in the co-weight lattice give rise to a real toric variety, called the real toric variety associated with the Weyl chambers. We compute the integral cohomology groups of real toric varieties associated with the Weyl chambers of type Cn and Dn, completing the computation for all classical types.

Keywords

real toric varietycohomologyroot systemWeyl chamberposet topologygeneralized Euler number

MSC classification

Primary: 14M25: Toric varieties, Newton polyhedra
Secondary: 57N65: Algebraic topology of manifolds 17B22: Root systems
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 3 , August 2019 , pp. 861 - 874
Copyright
Copyright © Edinburgh Mathematical Society 2019 

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