Deforming Curves in Jacobians to Non-Jacobians I: Curves in C (2)
نویسندگان
چکیده
منابع مشابه
Deforming Curves in Jacobians to Non-Jacobians I: Curves in C(2)
Abstract. 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 the second symmetric power C of C. More precisely, given a pencil g1 d of degree d on C, let X be the curve parametrizing pairs of points in divisors of g1 d (see the paper for the p...
متن کاملDeforming Curves in Jacobians to Non-jacobians I: Curves in C
Jacobians of curves are the best understood abelian varieties. There are many geometric ways of constructing curves in jacobians whereas it is difficult to construct interesting curves in most other abelian varieties. In this paper and its sequels we introduce methods for determining whether a given curve in a jacobian deforms with it when the jacobian deforms to a non-jacobian. We apply these ...
متن کاملDeforming Curves in Jacobians to Non-Jacobians II: Curves
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...
متن کاملCurves in Jacobians to Non - Jacobians Ii
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 کاملDeforming Curves Representing Multiples of the Minimal Class in Jacobians to Non-jacobians
Given a smooth nonhyperelliptic curve C and a pencil g d of degree d on C, let X be the curve parametrizing pairs of points in divisors of g d (see the paper for the precise scheme-theoretical definition). We prove that if X deforms infinitesimally out of the jacobian locus with JC then either d = 4 or d = 5, dimH(g 5 ) = 3 and C has genus 5 or genus 4 and only one g 3 .
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ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 2005
ISSN: 0046-5755,1572-9168
DOI: 10.1007/s10711-005-9006-3