Spherical varieties and Mori theory

DOI10.1215/S0012-7094-93-07213-4zbMath0821.14029MaRDI QIDQ1320595

Michel Brion

Publication date: 3 October 1995

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

stable curveNéron modelMori theoryflipsspherical varietycoloured faneffective 1-cycles

Mathematics Subject Classification ID

Homogeneous spaces and generalizations (14M17) Group actions on varieties or schemes (quotients) (14L30) Divisors, linear systems, invertible sheaves (14C20)

Related Items (31)

THE PSEUDO-INDEX OF HOROSPHERICAL FANO VARIETIES ⋮ Minimal generating system, essential divisors and \(G\)-desingularisation of toric varieties ⋮ Normality and smoothness of simple linear group compactifications ⋮ Spherical blow-ups of Grassmannians and Mori dream spaces ⋮ Equivariant degenerations of spherical modules for groups of type \(A\) ⋮ The generalized Mukai conjecture for symmetric varieties ⋮ On the algebraic stringy Euler number ⋮ On moment map and bigness of tangent bundles of \(G\)-varieties ⋮ Normality and non-normality of group compactifications in simple projective spaces ⋮ Embeddings of spherical homogeneous spaces ⋮ Sanya lectures: geometry of spherical varieties ⋮ The log minimal model program for horospherical varieties via moment polytopes ⋮ Automorphisms, root systems, and compactifications of homogeneous varieties ⋮ Effective and big divisors on a projective symmetric variety ⋮ Cohomologie des fibrés en droites sur les variétés magnifiques de rang minimal ⋮ The Lefschetz Principle in Birational Geometry: Birational Twin Varieties ⋮ A note about connectedness theorems à la Barth ⋮ Canonical singularities and horospherical actions ⋮ A combinatorial smoothness criterion for spherical varieties ⋮ Rational points on compactifications of semi-simple groups ⋮ Simple immersions of wonderful varieties ⋮ On the birational geometry of spaces of complete forms. II: Skew-forms ⋮ Pseudo-effective and nef cones on spherical varieties ⋮ On the geometry of spherical varieties ⋮ Gorenstein spherical Fano varieties ⋮ On Mori chamber and stable base locus decompositions ⋮ Complete symplectic quadrics and Kontsevich spaces of conics in Lagrangian Grassmannians ⋮ Effective divisors on Bott-Samelson varieties ⋮ Vanishing theorems for Dolbeault cohomology of log homogeneous varieties ⋮ The arc space of horospherical varieties and motivic integration ⋮ On reductive automorphism groups of regular embeddings

Cites Work

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• Valuations des espaces homogènes sphériques. (Valuations of spherical homogeneous spaces)
• Plongements d'espaces homogènes
• Vers une généralisation des espaces symétriques. (Towards a generalization of symmetric spaces)
• Groupe de Picard et nombres caractéristiques des variétés sphériques. (Picard group and characteristic numbers of spheric varieties.)
• Über gewisse G-stabile Teilmengen in projektiven Räumen. (On certain G-stable subsets in projective spaces)
• Complexity of action of reductive groups
• Espaces homogènes sphériques. (Spherical homogeneous spaces)
• Quelques propriétés des espaces homogènes sphériques. (Some properties of spherical homogeneous spaces)
• Normale Einbettungen von \(G/U\)
• On Hilbert's fourteenth problem for varieties of complexity one.
• Equivariant completion
• Fixed point schemes of additive group actions
• Some Basic Theorems on Algebraic Groups
• THE GEOMETRY OF TORIC VARIETIES

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