Results 1 to 10 of about 31,876 (167)
Picard Groups of Algebraic Groups and an Affineness Criterion
Comptes Rendus. Mathématique, 2023 We prove that an algebraic group over a field $k$ is affine precisely when its Picard group is torsion, and show that in this case the Picard group is finite when $k$ is perfect, and the product of a finite group of order prime to $p$ and a $p$-primary ...
Rosengarten, Zev
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The Picard group of Brauer-Severi varieties
Open Mathematics, 2018 In this paper, we provide explicit generators for the Picard groups of cyclic Brauer-Severi varieties defined over the base field. In particular,we provide such generators for all Brauer-Severi surfaces.
Badr Eslam +2 more
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Moduli spaces on the Kuznetsov component of Fano threefolds of index 2 [PDF]
Épijournal de Géométrie Algébrique, 2022 General hyperplane sections of a Fano threefold $Y$ of index 2 and Picard rank 1 are del Pezzo surfaces, and their Picard group is related to a root system.
Matteo Altavilla +2 more
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Towards quantized complex numbers: $q$-deformed Gaussian integers and the Picard group [PDF]
Open Communications in Nonlinear Mathematical Physics, 2021 This work is a first step towards a theory of "$q$-deformed complex numbers". Assuming the invariance of the $q$-deformation under the action of the modular group I prove the existence and uniqueness of the operator of translations by~$i$ compatible with
Valentin Ovsienko
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Smooth projective horospherical varieties of Picard group $\mathbb{Z}^2$ [PDF]
Épijournal de Géométrie Algébrique, 2020 We classify all smooth projective horospherical varieties of Picard group $\mathbb{Z}^2$ and we give a first description of their geometry via the Log Minimal Model Program.
Boris Pasquier
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On the GAGA principle for algebraic affine hypersurfaces
Comptes Rendus. Mathématique, 2022 For any complete $\mathbb{C}$-algebraic variety Y and its underlying compact $\mathbb{C}$-analytic space $\mathcal{Y}$, it follows from the well known GAGA principle that the algebraic Picard group $Pic(Y)$ and the analytic Picard group $\mathbb{P}\!ic ...
Tan, Vo Van
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The maximal unipotent finite quotient, unusual torsion in Fano threefolds, and exceptional Enriques surfaces [PDF]
Épijournal de Géométrie Algébrique, 2020 We introduce and study the maximal unipotent finite quotient for algebraic group schemes in positive characteristics. Applied to Picard schemes, this quotient encodes unusual torsion.
Andrea Fanelli, Stefan Schröer
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Polymorphic Automorphisms and the Picard Group
CoRR, 2021 16 pages.
Hofstra, Pieter +2 more
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Finite torsors over strongly $F$-regular singularities [PDF]
Épijournal de Géométrie Algébrique, 2022 We investigate finite torsors over big opens of spectra of strongly $F$-regular germs that do not extend to torsors over the whole spectrum. Let $(R,\mathfrak{m},k)$ be a strongly $F$-regular $k$-germ where $k$ is an algebraically closed field of ...
Javier Carvajal-Rojas
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Moduli space of rank one logarithmic connections over a compact Riemann surface
Comptes Rendus. Mathématique, 2020 Let $\mathcal{M}_X$ denote the moduli space of rank one logarithmic connections singular over a finite subset $S$ of a compact Riemann surface $X$ with fixed residues. We study the rational functions into $\mathcal{M}_X$. We prove that there is a natural
Singh, Anoop
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