Geodesic
Toric Surfaces with Reflection Symmetries
Informatics and Automation, Toric Topology, Group Actions, Geometry, and Combinatorics. Part 2, Tome 318 (2022), pp. 177-192

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $W$ be a reflection group in a plane and $P$ a rational polygon that is invariant under the $W$-action. The action of $W$ on $P$ induces a $W$-action on the toric variety $X_P$ associated with $P$. In this paper, we study the $W$-representation on the cohomology $H^*(X_P)$ and show that the invariant subring $H^*(X_P)^W$ is isomorphic to the cohomology ring of the toric variety associated with the fundamental region $P/W$. As an example, we provide an explicit description of the main result for the case of the toric variety associated with the fan of Weyl chambers of type $G_2$.
Keywords: toric variety, toric surface, reflection, singular cohomology. 
Jongbaek Song. Toric Surfaces with Reflection Symmetries. Informatics and Automation, Toric Topology, Group Actions, Geometry, and Combinatorics. Part 2, Tome 318 (2022), pp. 177-192. http://geodesic.mathdoc.fr/item/TRSPY_2022_318_a10/
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