منابع مشابه
Autoduality of the compactified Jacobian
We prove the following autoduality theorem for an integral projective curve C in any characteristic. Given an invertible sheaf L of degree 1, form the corresponding Abel map AL:C → J̄ , which maps C into its compactified Jacobian, and form its pullback map A L : Pic J̄ → J, which carries the connected component of 0 in the Picard scheme back to the Jacobian. If C has, at worst, points of multipli...
متن کاملThe compactified Picard scheme of the compactified Jacobian
Let C be an integral projective curve in any characteristic. Given an invertible sheaf L on C of degree 1, form the corresponding Abel map AL:C → J̄ , which maps C into its compactified Jacobian, and form its pullback map A L : Pic J̄ → J , which carries the connected component of 0 in the Picard scheme back to the Jacobian. If C has, at worst, double points, then A L is known to be an isomorphis...
متن کاملEuler number of the compactified Jacobian and
In this paper we show that the Euler number of the compactified Jacobian of a rational curve C with locally planar singularities is equal to the multiplicity of the δ-constant stratum in the base of a semi-universal deformation of C. In particular, the multiplicity assigned by Yau, Zaslow and Beauville to a rational curve on a K3 surface S coincides with the multiplicity of the normalisation ma...
متن کاملThe Picard Group of the Compactified Universal Jacobian
We determine explicitly the Picard groups of the universal Jacobian stack and of its compactification over the stack of stable curves. Along the way, we prove some results concerning the gerbe structure of the universal Jacobian stack over its rigidification by the natural action of the multiplicative group and relate this with the existence of generalized Poincaré line bundles. We also compare...
متن کاملGeometry of the theta divisor of a compactified jacobian
Contents 1. Introduction 1 1.1. Notation and Conventions 2 1.2. Brill-Noether varieties and Abel maps 4 1.3. Stability and semistability 6 2. Technical groundwork 9 2.1. Basic estimates 9 2.2. Basic cases 12 2.3. Divisors imposing independent conditions 14 3. Irreducibility and dimension 19 3.1. Irreducible components of the Theta divisor 19 3.2. Dimension of the image of the Abel map 24 4. Com...
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2002
ISSN: 0024-6107,1469-7750
DOI: 10.1112/s002461070100309x