Geodesic
Chow ring of horospherical varieties of Picard number one
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 38, Tome 513 (2022), pp. 147-163 
V. A. Petrov; A. K. Sonina. Chow ring of horospherical varieties of Picard number one. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 38, Tome 513 (2022), pp. 147-163. http://geodesic.mathdoc.fr/item/ZNSL_2022_513_a10/
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     author = {V. A. Petrov and A. K. Sonina},
     title = {Chow ring of horospherical varieties of {Picard} number one},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_513_a10/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

An algorithm based on Goresky–Kottwitz–MacPherson method is provided to compute the equivariant Chow ring of a horospherical variety of Picard number one. In the case of $G_2$-variety, an explicit presentation of this ring is given.

[1] M. Brion, “Equivariant Chow groups for torus actions”, Transformation Groups, 2:3 (1997), 225–267 | DOI | MR

[2] D. Edidin and W. Graham, “Localization in equivariant intersection theory and the Bott residue formula”, Amer. J. Math., 120 (1998), 619–636 | DOI | MR

[3] W. Fulton, Intersection theory, Second edition, Springer-Verlag, Berlin, 1998 | MR

[4] R. Gonzales, C. Pech, N. Perrin, and A. Samokhin, Geometry of horospherical varieties of Picard rank one, IMRN, 2021 | MR

[5] M. Goresky, R. Kottwitz and R. MacPherson, “Equivariant cohomology, Koszul duality, and the localization theorem”, Invent. math., 131 (1998), 25–83 | DOI | MR

[6] B. Pasquier, “On some smooth projective two-orbit varieties with Picard number $1$”, Math. Ann., 344 (2009), 963–987 | DOI | MR

[7] B. Pasquier, L. Manivel, Horospherical two-orbit varieties as zero loci, Hal-Id: hal-03048217, 2020

[8] Julianna S. Tymoczko, Divided difference operators for partial flag varieties, 2009, arXiv: math/0912.2545v1