Displaying similar documents to “A Torelli theorem for moduli spaces of principal bundles over a curve”

Orthogonal bundles on curves and theta functions

Arnaud Beauville (2006)

Annales de l’institut Fourier

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Let ℳ be the moduli space of principal SO r -bundles on a curve C , and ℒ the determinant bundle on ℳ . We define an isomorphism of H 0 ( ℳ , ℒ ) onto the dual of the space of r -th order theta functions on the Jacobian of C . This isomorphism identifies the rational map ℳ ⇢ | ℒ | * defined by the linear system | ℒ | with the map ℳ ⇢ | r Θ | which associates to a quadratic bundle ( E , q ) the theta divisor Θ E . The two components ℳ + and ℳ - of ℳ are mapped into the subspaces of even and odd theta functions respectively. Finally we discuss...

About G -bundles over elliptic curves

Yves Laszlo (1998)

Annales de l'institut Fourier

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Let G be a complex algebraic group, simple and simply connected, T a maximal torus and W the Weyl group. One shows that the coarse moduli space M G ( X ) parametrizing S -equivalence classes of semistable G -bundles over an elliptic curve X is isomorphic to [ Γ ( T ) ⊗ Z X ] / W . By a result of Looijenga, this shows that M G ( X ) is a weighted projective space.

Numerical character of the effectivity of adjoint line bundles

Frédéric Campana, Vincent Koziarz, Mihai Păun (2012)

Annales de l’institut Fourier

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In this note we show that, for any log-canonical pair ( X , Δ ) , K X + Δ is ℚ -effective if its Chern class contains an effective ℚ -divisor. Then, we derive some direct corollaries.

Unramified Brauer group of the moduli spaces of PGLr(ℂ)-bundles over curves

Indranil Biswas, Amit Hogadi, Yogish Holla (2014)

Open Mathematics

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Let X be an irreducible smooth complex projective curve of genus g, with g ≥ 2. Let N be a connected component of the moduli space of semistable principal PGLr (ℂ)-bundles over X; it is a normal unirational complex projective variety. We prove that the Brauer group of a desingularization of N is trivial.

The Frobenius action on rank 2 vector bundles over curves in small genus and small characteristic

Laurent Ducrohet (2009)

Annales de l’institut Fourier

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Let X be a general proper and smooth curve of genus 2 (resp. of genus 3 ) defined over an algebraically closed field of characteristic p . When 3 ≤ p ≤ 7 , the action of Frobenius on rank 2 semi-stable vector bundles with trivial determinant is completely determined by its restrictions to the 30 lines (resp. the 126 Kummer surfaces) that are invariant under the action of some order 2 line bundle over X . Those lines (resp. those Kummer surfaces) are closely related to the elliptic curves (resp....