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193
DEMAZURE ROOTS AND SPHERICAL VARIETIES: THE EXAMPLE OF HORIZONTAL SL2ACTIONS
, 2014
"... Let G be a connected reductive group, and let X be an affine Gspherical variety. We show that the classification of Gaactions on X normalized by G can be reduced to the description of quasiaffine homogeneous spaces under the action of a semidirect product Ga ⋊ G with the following property. Th ..."
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Cited by 2 (1 self)
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Let G be a connected reductive group, and let X be an affine Gspherical variety. We show that the classification of Gaactions on X normalized by G can be reduced to the description of quasiaffine homogeneous spaces under the action of a semidirect product Ga ⋊ G with the following property
Classification of smooth affine spherical varieties
"... Let G be a complex reductive group. A normal Gvariety X is called spherical if a Borel subgroup of G has a dense orbit in X. Of particular interest are spherical varieties which are smooth and affine since they form local models for multiplicity free Hamiltonian Kmanifolds, K a maximal compact sub ..."
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Cited by 14 (1 self)
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Let G be a complex reductive group. A normal Gvariety X is called spherical if a Borel subgroup of G has a dense orbit in X. Of particular interest are spherical varieties which are smooth and affine since they form local models for multiplicity free Hamiltonian Kmanifolds, K a maximal compact
Toric Degenerations of Spherical Varieties
 SELECTA MATH. (N.S
, 2004
"... We prove that any affine, resp. polarized projective, spherical variety admits a flat degeneration to an affine, resp. polarized projective, toric variety. Motivated by Mirror Symmetry, we give conditions for the limit toric variety to be a Gorenstein Fano, and provide many examples. We also provid ..."
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Cited by 40 (0 self)
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We prove that any affine, resp. polarized projective, spherical variety admits a flat degeneration to an affine, resp. polarized projective, toric variety. Motivated by Mirror Symmetry, we give conditions for the limit toric variety to be a Gorenstein Fano, and provide many examples. We also
Spherical varieties and Langlands duality
, 2004
"... Abstract. Let G be a connected reductive complex algebraic group. This paper is devoted to the space Z of meromorphic quasimaps from a curve into an affine spherical Gvariety X. The space Z may be thought of as an algebraic model for the loop space of X. The theory we develop associates to X a conn ..."
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Cited by 8 (2 self)
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Abstract. Let G be a connected reductive complex algebraic group. This paper is devoted to the space Z of meromorphic quasimaps from a curve into an affine spherical Gvariety X. The space Z may be thought of as an algebraic model for the loop space of X. The theory we develop associates to X a
Boundedness of spherical Fano varieties
, 2003
"... Classically, G. Fano proved that the family of (smooth, anticanonically embedded) Fano 3dimensional varieties is bounded, and moreover provided their classification, later completed by V.A. Iskovskikh, S. Mukai and S. Mori. For singular Fano varieties with log terminal singularities, there are two ..."
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Cited by 2 (0 self)
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basic boundedness conjectures: Index Boundedness and the much stronger ǫlt Boundedness. The ǫlt Boundedness was known only in two cases: in dimension 2 [Ale94] and for toric varieties [BB93]. In this paper we prove it for a significantly less “elementary ” class, that of spherical varieties
The LunaVust theory of spherical embeddings
 in Proc. of the Hyderabad Conf. on Algebraic Groups, Manoj Prakashan
, 1991
"... the importance of a very distinguished class of homogeneous varieties G/H, those which are now called spherical. Such varieties are homogeneous for a connected reductive group G and are characterized by many equivalent properties, the most important being (see [BLV]): — Any Borel subgroup B of G has ..."
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Cited by 87 (2 self)
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Procesi [CP]... (symmetric varieties) and Pauer [Pau1] (horospherical varieties). The last case appeared already as an application of the general theory of Luna and Vust on embeddings of arbitrary homogeneous varieties. Unfortunately, in [LV] the classification of embeddings of spherical varieties is buried
Affine varieties with equivalent cylinders
 J. Algebra
"... Abstract. A wellknown cancellation problem asks when, for two algebraic varieties V 1 , V 2 ⊆ C n , the isomorphism of the cylinders V 1 × C and V 2 × C implies the isomorphism of V 1 and V 2 . In this paper, we address a related problem: when the equivalence (under an automorphism of C n+1 ) of t ..."
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Cited by 9 (5 self)
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Abstract. A wellknown cancellation problem asks when, for two algebraic varieties V 1 , V 2 ⊆ C n , the isomorphism of the cylinders V 1 × C and V 2 × C implies the isomorphism of V 1 and V 2 . In this paper, we address a related problem: when the equivalence (under an automorphism of C n+1
On Orbit Closures Of Spherical Subgroups In Flag Varieties
 COMMENT. MATH. HELV
"... Let F be the flag variety of a complex semisimple group G, let H be an algebraic subgroup of G acting on F with nitely many orbits, and let V be an Horbit closure in F . Expanding the cohomology class of V in the basis of Schubert classes defines a union V 0 of Schubert varieties in F with pos ..."
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Cited by 31 (3 self)
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Let F be the flag variety of a complex semisimple group G, let H be an algebraic subgroup of G acting on F with nitely many orbits, and let V be an Horbit closure in F . Expanding the cohomology class of V in the basis of Schubert classes defines a union V 0 of Schubert varieties in F
ADDITIVE GROUP ACTIONS ON AFFINE TVARIETIES OF COMPLEXITY ONE IN ARBITRARY CHARACTERISTIC
"... ar ..."
A COMBINATORIAL SMOOTHNESS CRITERION FOR SPHERICAL VARIETIES
, 2013
"... We present a combinatorial criterion for the smoothness of an arbitrary spherical variety. This generalizes an earlier result due to Camus for spherical varieties of type A. ..."
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We present a combinatorial criterion for the smoothness of an arbitrary spherical variety. This generalizes an earlier result due to Camus for spherical varieties of type A.
Results 1  10
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193