Abstract
We study intersection numbers of invariant divisors in the toric manifold associated with the fan determined by the collection of Weyl chambers for each root system of classical type and of exceptional type $G_2$. We give a combinatorial formula for intersection numbers of certain subvarieties which are naturally indexed by elements of the Weyl group. These numbers describe the ring structure of the cohomology of the toric manifold.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
6 articles.
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1. Toric Surfaces with Reflection Symmetries;Proceedings of the Steklov Institute of Mathematics;2022-09
2. Торические поверхности, симметричные относительно отражений;Trudy Matematicheskogo Instituta imeni V.A. Steklova;2022-09
3. Generic torus orbit closures in Schubert varieties;Journal of Combinatorial Theory, Series A;2020-02
4. A Survey of Recent Developments on Hessenberg Varieties;Springer Proceedings in Mathematics & Statistics;2020
5. The Cohomology Groups of Real Toric Varieties Associated with Weyl Chambers of TypesCandD;Proceedings of the Edinburgh Mathematical Society;2019-02-14