Relevant bibliographies by topics / Parabolic subgroups, projective homogeneous varieties

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Academic literature on the topic 'Parabolic subgroups, projective homogeneous varieties'

Author: Grafiati
Published: 21 September 2024

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Journal articles on the topic "Parabolic subgroups, projective homogeneous varieties"

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Biswas, Indranil, Krishna Hanumanthu, and D. S. Nagaraj. "Positivity of vector bundles on homogeneous varieties." International Journal of Mathematics 31, no. 12 (2020): 2050097. http://dx.doi.org/10.1142/s0129167x20500974.

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We study the following question: Given a vector bundle on a projective variety [Formula: see text] such that the restriction of [Formula: see text] to every closed curve [Formula: see text] is ample, under what conditions [Formula: see text] is ample? We first consider the case of an abelian variety [Formula: see text]. If [Formula: see text] is a line bundle on [Formula: see text], then we answer the question in the affirmative. When [Formula: see text] is of higher rank, we show that the answer is affirmative under some conditions on [Formula: see text]. We then study the case of [Formula: s
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2

Lazar, Youssef. "On the density of S-adic integers near some projective G-varieties." Annales Fennici Mathematici 48, no. 1 (2023): 187–204. http://dx.doi.org/10.54330/afm.127001.

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We provide some general conditions which ensure that a system of inequalities involving homogeneous polynomials with coefficients in a \(S\)-adic field has nontrivial \(S\)-integral solutions. The proofs are based on the strong approximation property for Zariski-dense subgroups and adelic geometry of numbers. We give some examples of applications for systems involving quadratic and linear forms.
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3

Brion, Michel, and Aloysius G. Helminck. "On Orbit Closures of Symmetric Subgroups in Flag Varieties." Canadian Journal of Mathematics 52, no. 2 (2000): 265–92. http://dx.doi.org/10.4153/cjm-2000-012-9.

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AbstractWe study K-orbits in G/P where G is a complex connected reductive group, P ⊆ G is a parabolic subgroup, and K ⊆ G is the fixed point subgroup of an involutive automorphism θ. Generalizing work of Springer, we parametrize the (finite) orbit set K \ G/P and we determine the isotropy groups. As a consequence, we describe the closed (resp. affine) orbits in terms of θ-stable (resp. θ-split) parabolic subgroups. We also describe the decomposition of any (K, P)-double coset in G into (K, B)-double cosets, where B ⊆ P is a Borel subgroup. Finally, for certain K-orbit closures X ⊆ G/B, and for
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4

Fresse, Lucas, and Ivan Penkov. "On Homogeneous Spaces for Diagonal Ind-Groups." Transformation Groups, April 25, 2024. http://dx.doi.org/10.1007/s00031-024-09853-4.

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AbstractWe study the homogeneous ind-spaces $$\textrm{GL}(\textbf{s})/\textbf{P}$$ GL ( s ) / P where $$\textrm{GL}(\textbf{s})$$ GL ( s ) is a strict diagonal ind-group defined by a supernatural number $$\textbf{s}$$ s and $$\textbf{P}$$ P is a parabolic ind-subgroup of $$\textrm{GL}(\textbf{s})$$ GL ( s ) . We construct an explicit exhaustion of $$\textrm{GL}(\textbf{s})/\textbf{P}$$ GL ( s ) / P by finite-dimensional partial flag varieties. As an application, we characterize all locally projective $$\textrm{GL}(\infty )$$ GL ( ∞ ) -homogeneous spaces, and some direct products of such spaces
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Franceschini, Alberto, and Luis E. Solá Conde. "Inversion maps and torus actions on rational homogeneous varieties." Geometriae Dedicata 218, no. 1 (2023). http://dx.doi.org/10.1007/s10711-023-00866-z.

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AbstractComplex projective algebraic varieties with $${{\mathbb {C}}}^*$$ C ∗ -actions can be thought of as geometric counterparts of birational transformations. In this paper we describe geometrically the birational transformations associated to rational homogeneous varieties endowed with a $${{\mathbb {C}}}^*$$ C ∗ -action with no proper isotropy subgroups.
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Gorodnik, Alexander, Jialun Li та Cagri Sert. "Stationary measures for SL2(ℝ)-actions on homogeneous bundles over flag varieties". Journal für die reine und angewandte Mathematik (Crelles Journal), 26 липня 2024. http://dx.doi.org/10.1515/crelle-2024-0043.

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Abstract Let 𝐺 be a real semisimple Lie group with finite centre and without compact factors, Q < G Q<G a parabolic subgroup and 𝑋 a homogeneous space of 𝐺 admitting an equivariant projection on the flag variety G / Q G/Q with fibres given by copies of lattice quotients of a semisimple factor of 𝑄. Given a probability measure 𝜇, Zariski-dense in a copy of H = SL 2 ⁡ ( R ) H=\operatorname{SL}_{2}(\mathbb{R}) in 𝐺, we give a description of 𝜇-stationary probability measures on 𝑋 and prove corresponding equidistribution results. Contrary to the results of Benoist–Quint corresponding to the c
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Dissertations / Theses on the topic "Parabolic subgroups, projective homogeneous varieties"

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Maccan, Matilde. "Sous-schémas en groupes paraboliques et variétés homogènes en petites caractéristiques." Electronic Thesis or Diss., Université de Rennes (2023-....), 2024. https://ged.univ-rennes1.fr/nuxeo/site/esupversions/2e27fe72-c9e0-4d56-8e49-14fc84686d6c.

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Cette thèse achève la classification des sous-schémas en groupes paraboliques des groupes algébriques semi-simples sur un corps algébriquement clos, en particulier de caractéristique deux et trois. Dans un premier temps, nous présentons la classification en supposant que la partie réduite de ces sous-groupes soit maximale, avant de passer au cas général. Nous parvenons à une description quasiment uniforme : à l'exception d'un groupe de type G₂ en caractéristique deux, chaque sous-schémas en groupes parabolique est obtenu en multipliant des paraboliques réduits par des noyaux d'isogénies pureme
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