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Groupe de Picard et nombres caractéristiques des variétés sphériques. (Picard group and characteristic numbers of spheric varieties.). (French) Zbl 0701.14052
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

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
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