منابع مشابه
Simpson Jacobians of Reducible Curves
For any projective curve X let M d (X) be the Simpson moduli space of pure dimension one rank 1 degree d sheaves that are semistable with respect to a fixed polarization H on X . When X is a reduced curve the connected component of M d (X) that contains semistable line bundles can be considered as the compactified Jacobian of X . In this paper we give explicitly the structure of this compactifi...
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The compactified Jacobian of any projective curve X is defined as the Simpson moduli space of torsion free rank one degree d sheaves that are semistable with respect to a fixed polarization H on X. In this paper we give explicitly the structure of this compactified Simpson Jacobian in the case where X is a generalized tree-like curve, i.e., a projective, reduced and connected curve such that th...
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We introduce deformation theoretic methods for determining when a curve X in a nonhyperelliptic Jacobian JC will deform with JC to a non-Jacobian. We apply these methods to a particular class of curves in symmetric powers C of C where 3 e g−3. More precisely, given a pencil g1 d of degree d on C, let X be the curve parametrizing divisors of degree e in divisors of g1 d (see the paper for the pr...
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This is a second paper where we introduce deformation theory methods which can be applied to finding curves in families of principally polarized abelian varieties (ppav) containing jacobians. One of our motivations for finding interesting and computationally tractable curves in ppav is to solve the Hodge conjecture for the primitive cohomology of the theta divisor which we explain below. For ot...
متن کاملDecomposing Jacobians of Hyperelliptic Curves
Many interesting questions can be asked about the decomposition of Jacobians of curves. For instance, we may want to know which curves have completely decomposable Jacobians (Jacobians which are the product of g elliptic curves) [4]. We may ask about number theoretic properties of the elliptic curves that show up in the decomposition of Jacobians of curves [2]. We would also like to know how ma...
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ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2005
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crll.2005.2005.582.1