منابع مشابه
Hecke transformation for orthogonal bundles and stability of Picard bundles
Given a holomorphic vector bundle F over a compact Riemann surface X, and a subspace Sx ⊂ Fx in the fiber over a point x, the Hecke transformation produces a new vector bundle E on X [10, 16]. The vector bundle E is the kernel of the natural quotient map F −→ Fx/Sx. Hecke transformation is a very useful tool to study the moduli space. For instance, they are used in computation of cohomologies o...
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Let P be the Prym variety associated with a covering π : Y → X between non-singular irreducible projective curves. If P̃ is a principally polarized Prym-Tyurin variety associated with P , we prove that the induced Abel-Prym morphism ρ̃ : Y → P̃ is birational onto its image for genus gX > 2 and deg π 6= 2. We use such result to prove that the Picard bundle over the Prym variety is simple and moreov...
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Let X be an irreducible smooth projective curve of genus g ≥ 3 defined over the complex numbers and let Mξ denote the moduli space of stable vector bundles on X of rank n and determinant ξ, where ξ is a fixed line bundle of degree d. If n and d have a common divisor, there is no universal vector bundle on X ×Mξ. We prove that there is a projective bundle on X ×Mξ with the property that its rest...
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Introduction. The purpose of this note is to show a relation between the syzygies of a curve completely embedded by its canonical bundle and the Ext-cohomology of Picard bundles on its Jacobian. The spirit of the result is to try to interpret geometrically Green’s conditions Np on the jacobian rather than on the curve. In order to describe the result, we need some preliminary material and notat...
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Let G be a simple simply-connected connected complex affine algebraic group and let C be a smooth irreducible projective curve of genus ≥ 2 over the field of complex numbers C. Let M be the moduli space of semistable principal G-bundles on C and let Pic M be its Picard group, i.e., the group of isomorphism classes of algebraic line bundles on M. Following is our main result (which generalizes a...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1961
ISSN: 0019-2082
DOI: 10.1215/ijm/1255631580