Simple immersions of wonderful varieties

Pezzini, Guido

doi:10.1007/s00209-006-0050-y

Cited by 10 publications

(9 citation statements)

References 12 publications

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“…The variety X D was studied by G. Pezzini in [39] when D is ample, that is, D ∈ N >0 ∆. Under this assumption, either X D is isomorphic to M or it is not even normal.…”

Section: On the Normality Of Spherical Orbit Closures In Simple Projementioning

confidence: 99%

Projective normality of model varieties and related results

2016

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Abstract. We prove that the multiplication of sections of globally generated line bundles on a model wonderful variety M of simply connected type is always surjective. This follows by a general argument which works for every wonderful variety and reduces the study of the surjectivity for every couple of globally generated line bundles to a finite number of cases. As a consequence, the cone defined by a complete linear system over M or over a closed G-stable subvariety of M is normal. We apply these results to the study of the normality of the compactifications of model varieties in simple projective spaces and of the closures of the spherical nilpotent orbits. Then we focus on a particular case proving two specific conjectures of Adams, Huang and Vogan on an analogue of the model orbit of the group of type E 8 .

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“…The variety X D was studied by G. Pezzini in [39] when D is ample, that is, D ∈ N >0 ∆. Under this assumption, either X D is isomorphic to M or it is not even normal.…”

Section: On the Normality Of Spherical Orbit Closures In Simple Projementioning

confidence: 99%

Projective normality of model varieties and related results

2016

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“…(14) M is said to be strict if the stabilizer of any point is self-normalizing; equivalently, we will say also that H is strict. A wonderful variety is strict if and only if it can be embedded in a simple projective space (see [Pe2]). (15) Consider the following sets of spherical roots…”

Section: Preliminariesmentioning

confidence: 99%

“…Our main theorem (Theorem 5.9) is a combinatorial criterion for X → X to be bijective; this is done under the assumption that M is strict, i.e. that all isotropy groups of M are self-normalizing: strict wonderful varieties, introduced in [Pe2], are those wondeful varieties which can be embedded in a simple projective space; they form an important class of wonderful varieties which generalize the symmetric ones of [CP]. The condition of bijectivity involves the double links of the Dynkin diagram of G and it is trivially fulfilled whenever G is simply laced or M is symmetric; it is easily read off by the spherical diagram of M , which is a useful tool to represent a wonderful variety starting from the Dynkin diagram of G. Main examples of strict wonderful varieties where bijectivity fails arise from the context of wonderful model varieties introduced in [Lu3]; the general strict case is substantially deduced from the model case.…”

Section: Introductionmentioning

confidence: 99%

Spherical orbit closures in simple projective spaces and their normalizations

Gandini

2011

Transformation Groups

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Let G be a simply connected semisimple algebraic group over an algebraically closed field k of characteristic 0 and let V be a rational simple G-module. If G/H is a spherical orbit in P(V) and if X = G/H is its closure, then we describe the orbits of X and those of its normalization Y. If, moreover, the wonderful completion of G/H is strict, then we give necessary and sufficient combinatorial conditions so that the normalization morphism Y --> X is a homeomorphism. Such conditions are trivially fulfilled if G is simply laced or if H is a symmetric subgroup

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“…G. Pezzini has shown in [Pe07] that the closure of G. [x] in P(V π ) is wonderful if and only if S is strict and supp (δ) = .…”

Section: Spherical Orbits In Simple Projective Spacesmentioning

confidence: 98%