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Spherical varieties

Webgeneral spherical varieties. Remark 1.1. The de nitions of m geom(ˇ;˜) and I geom(f) are very similar to each other. So one only needs to de ne m geom(ˇ;˜) for general spherical varieties, which will lead to the de nition of I geom(f). In this paper, we propose a uniform de nition of m geom(ˇ;˜) (and hence I geom(f)) for general spherical ... WebA normal G-variety 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 K-manifolds, K a maximal compact subgroup of G.

On the unramified spectrum of spherical varieties over

WebSymmetric varieties are normal equivarient open embeddings of symmetric homogeneous spaces, and they are interesting examples of spherical varieties. We prove that all smooth Fano symmetric varieties with Picard number one admit Kähler–Einstein metrics by using a combinatorial criterion for K-stability of Fano spherical varieties … WebThe theory of wonderful varieties is developed in §30. Applications include computation of the canonical divisor of a spherical variety and Luna’s conceptual approach to the … cranbrook kijiji heavy equipment https://seelyeco.com

Spherical varieties and tropical geometry

Web10. júl 2024 · Spherical varieties (spherical homogeneous spaces and spherical embeddings) were considered in works of Luna, Vust, Brion, Knop, Losev, and others. The classification of spherical homogeneous spaces over algebraically closed fields of characteristic $0$ was completed in the works of Losev [ 37 ] and Bravi and Pezzini [ 13 … WebEvery flag variety, and indeed every projective variety homogeneous under a linear algebraic group, is a Mori Dream Space. In fact, there is a class of varieties that contains both projective homogeneous varieties and toric varieties (another large class of Mori Dream Spaces), namely "spherical varieties". WebA nice feature of a spherical homogeneous space is that any embedding of it (called a spherical variety) contains only finitely many G-orbits, and these are themselves … cranbrook kijiji bc

Spherical varieties - University of Texas at Austin

Category:[1702.08264] The dual group of a spherical variety - arXiv.org

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Spherical varieties

Spherical Varieties SpringerLink

Web29. sep 2024 · We review some aspects of the geometry of spherical varieties. We first describe the structure of B-orbits. Using the local structure theorems, we describe the … WebIn short, the visibility is a geometric condition that assures the multiplicity-freeness property. In this article we consider the converse direction when U U is a compact real form of a connected complex reductive algebraic group G G and X X is an irreducible complex algebraic G G -variety. In this setting the multiplicity-freeness property of ...

Spherical varieties

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WebTY - JOUR AU - Bravi, Paolo TI - Classification of spherical varieties JO - Les cours du CIRM PY - 2010 PB - CIRM VL - 1 IS - 1 SP - 99 EP - 111 AB - We give a short introduction to the problem of classification of spherical varieties, by presenting the Luna conjecture about the classification of wonderful varieties and illustrating some of the ... WebThese notes contain an introduction to the theory of spherical and wonderful varieties. We describe the Luna-Vust theory of embeddings of spherical homogeneous spaces, and explain how wonderful varieties fit in the theory. How to cite MLA BibTeX RIS Pezzini, Guido. "Lectures on spherical and wonderful varieties."

Web8 CHAPTER 1. PRINCIPAL BUNDLES Proof. The ring A is integrally closed over AG.Indeed, for a 2 A, we have the equation Y g2G (a¡g ¢a):Let a1;¢¢¢an be generators of A as an … WebSpherical varieties, functoriality, and quantization. Submitted to the Proceedings of the 2024 ICM, 44pp. 2009.03943 : Intersection complexes and unramified L-factors. (With Jonathan …

Web1. Spherical varieties 1.1. What is a spherical variety? A G-variety Xover F qis called spherical if X kis a normal variety with an open dense orbit of a Borel B kˆG k after base change to k. One should think of this as a niteness property. For example, Brion proved the above de nition is equivalent to X k having nitely many B k orbits. The ... Spherical embeddings are classified by so-called colored fans, a generalization of fans for toric varieties; this is known as Luna-Vust Theory. In his seminal paper, Luna (2001) developed a framework to classify complex spherical subgroups of reductive groups; he reduced the classification of spherical subgroups to wonderful subgroups.

WebSpherical varieties A complex algebraic variety is a spherical variety if it’s acted upon by a reductive group G and there is a dense orbit under the action of a Borel subgroup B. Reductive groups include semisimple groups (e.g., SL n, symplectic groups, orthogonal groups), tori (C)n, and general linear groups.

Web19. jan 2003 · Boundedness of spherical Fano varieties. We prove that for any e>0, there exists only finitely many e-log terminal spherical Fano varieties of fixed dimension. We also introduce an invariant of a spherical subgroup H in a reductive group G which measures how nice an equivariant Fano compactification G/H there exists. cranbrook kijiji garage salesWeb12 May - 18 May 2013. This workshop brought together, for the first time, experts on spherical varieties and experts on automorphic forms, in order to discuss subjects of common interest between the two fields. Spherical varieties have a very rich and deep structure, which leads one to attach certain root systems and, eventually, a “Langlands ... استهلاك الوقود راف فور 2022 هايبردWebIn particular, we discuss the close relationship between log homogeneous varieties and spherical varieties, and we survey classical examples of spherical homogeneous spaces … cranbrook kijiji petsWeb29. feb 2012 · In its initial conception, as given in the book [102] of Sakellaridis-Venkatesh, the relative Langlands program is concerned with a spherical subgroup H ⊂ G, so that X = H\G is a spherical... cranbrook kijiji carsWeb29. nov 2011 · In a recent preprint, Sakellaridis and Venkatesh considered the spectral decomposition of the space , where $X = H\G$ is a spherical variety and is a real or -adic group, and stated a conjecture describing this decomposition in terms of a … cranbrook mcdonald\\u0027sWeb14. nov 2024 · A spherical variety is a normal variety X together with an action of a connected reductive affine algebraic group G, a Borel subgroup B ⊂ G, and a base point x 0 ∈ X such that the B -orbit of x 0 in X is a dense open subset of X. cranbrook jamaicaWebAccording to a talk by Domingo Luna around 1985, the term spherical variety is not derived from spheres, at least not directly. Firstly, spheres are way too atypical, e.g., their … cranbrook mini golf