About $G$-bundles over elliptic curves

Yves Laszlo

Displaying similar documents to “About $G$ -bundles over elliptic curves”

A criterion for virtual global generation

Indranil Biswas, A. J. Parameswaran (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let $X$ be a smooth projective curve defined over an algebraically closed field $k$ , and let $F_{X}$ denote the absolute Frobenius morphism of $X$ when the characteristic of $k$ is positive. A vector bundle over $X$ is called virtually globally generated if its pull back, by some finite morphism to $X$ from some smooth projective curve, is generated by its global sections. We prove the following. If the characteristic of $k$ is positive, a vector bundle $E$ over $X$ is virtually globally generated if and only...

Poincaré bundles for projective surfaces

Nicole Mestrano (1985)

Annales de l'institut Fourier

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Let $X$ be a smooth projective surface, $K$ the canonical divisor, $H$ a very ample divisor and $M_{H} (c_{1}, c_{2})$ the moduli space of rank-two vector bundles, $H$ -stable with Chern classes $c_{1}$ and $c_{2}$ . We prove that, if there exists $c_{1}^{'}$ such that $c_{1}$ is numerically equivalent to $2 c_{1}^{'}$ and if $c_{2} - \frac{1}{4} c_{1}^{2}$ is even, greater or equal to $H^{2} + H K + 4$ , then there is no Poincaré bundle on $M_{H} (c_{1}, c_{2}) \times X$ . Conversely, if there exists $c_{1}^{'}$ such that the number $c_{1}^{'} \cdot c_{1}$ is odd or if $\frac{1}{2} c_{1}^{2} - \frac{1}{2} c_{1} \cdot K - c_{2}$ is odd, then there exists a Poincaré bundle on $M_{H} (c_{1}, c_{2}) \times X$ .

Trivial noncommutative principal torus bundles

Stefan Wagner (2011)

Banach Center Publications

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A (smooth) dynamical system with transformation group ⁿ is a triple (A,ⁿ,α), consisting of a unital locally convex algebra A, the n-torus ⁿ and a group homomorphism α: ⁿ → Aut(A), which induces a (smooth) continuous action of ⁿ on A. In this paper we present a new, geometrically oriented approach to the noncommutative geometry of trivial principal ⁿ-bundles based on such dynamical systems, i.e., we call a dynamical system (A,ⁿ,α) a trivial noncommutative principal ⁿ-bundle if each isotypic...

Degenerations of moduli of stable bundles over algebraic curves

Huashi Xia (1995)

Compositio Mathematica

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The line bundles on the moduli of parabolic $G$ -bundles over curves and their sections

Yves Laszlo, Christoph Sorger (1997)

Annales scientifiques de l'École Normale Supérieure

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On moduli of $G$ -bundles of a curve for exceptional $G$

Christoph Sorger (1999)

Annales scientifiques de l'École Normale Supérieure

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Product preserving gauge bundle functors on vector bundles

Włodzimierz M. Mikulski (2001)

Colloquium Mathematicae

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A complete description is given of all product preserving gauge bundle functors F on vector bundles in terms of pairs (A,V) consisting of a Weil algebra A and an A-module V with $d i m_{ℝ} (V) < \infty$ . Some applications of this result are presented.

Bounds for Chern classes of semistable vector bundles on complex projective spaces

Wiera Dobrowolska (1993)

Colloquium Mathematicae

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This work concerns bounds for Chern classes of holomorphic semistable and stable vector bundles on $ℙ^{n}$ . Non-negative polynomials in Chern classes are constructed for 4-vector bundles on $ℙ^{4}$ and a generalization of the presented method to r-bundles on $ℙ^{n}$ is given. At the end of this paper the construction of bundles from complete intersection is introduced to see how rough the estimates we obtain are.

Displaying similar documents to “About G -bundles over elliptic curves”

Displaying similar documents to “About $G$ -bundles over elliptic curves”