Geometry of the theta divisor of a compactified jacobian

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Geometry 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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Very ampleness for Theta on the compactified Jacobian

It follows from [14, Section 17, p. 163] that 3Θ is very ample. In the singular case, D’Souza has constructed a natural compactification J̄0 for the Jacobian J0 of a complete, integral curve over an algebraically closed field [5]. The scheme J̄0 parametrizes torsion-free, rank 1 sheaves of Euler characteristic 0 on X . A natural question in this context is whether there is a canonical Cartier div...

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Autoduality of the compactified Jacobian

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The 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...

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Euler 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...

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ژورنال

عنوان ژورنال: Journal of the European Mathematical Society

سال: 2009

ISSN: 1435-9855

DOI: 10.4171/jems/185