Brion, Michel Groupe de Picard et nombres caractéristiques des variétés sphériques. (Picard group and characteristic numbers of spheric varieties.). (French) Zbl 0701.14052 Duke Math. J. 58, No. 2, 397-424 (1989). Let X be a normal algebraic variety over an algebraically closed field of characteristic zero and G a reductive connected algebraic group acting on X. X is called a spheric variety if there is a Borel subgroup of G with a dense orbit in X. This notion generalizes that of symmetric varieties [see C. De Concini and C. Procesi in Invariant theory, Proc. 1st 1982 Sess. C.I.M.E., Montecatini/Italy, Lect. Notes Math. 996, 1-44 (1983; Zbl 0581.14041)]. The paper under review describes the Picard group of spherical varieties, as well as the intersection numbers of their divisors. As customary, some applications to classical examples are given, and so, characteristic numbers for linear spaces, flags and plane and space conics are, once again, computed. Reviewer: E.Casas-Alvero Cited in 6 ReviewsCited in 79 Documents MSC: 14N10 Enumerative problems (combinatorial problems) in algebraic geometry 14M17 Homogeneous spaces and generalizations 14L30 Group actions on varieties or schemes (quotients) 14C22 Picard groups Keywords:spheric variety; Borel subgroup; dense orbit; symmetric varieties; Picard group of spherical varieties; intersection numbers; characteristic numbers Citations:Zbl 0581.14041 PDFBibTeX XMLCite \textit{M. Brion}, Duke Math. J. 58, No. 2, 397--424 (1989; Zbl 0701.14052) Full Text: DOI References: [1] M. F. Atiyah and R. Bott, The moment map and equivariant cohomology , Topology 23 (1984), no. 1, 1-28. · Zbl 0521.58025 [2] E. Akyildiz and J. B. Carrell, An algebraic formula for the Gysin homomorphism from \(G/B\) to \(G/P\) , Illinois J. Math. 31 (1987), no. 2, 312-320. · Zbl 0629.57030 [3] S. Abeasis, A. DelFra, and H. Kraft, The geometry of representations of \(A\sbm\) , Math. 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