Deforming Curves in Jacobians to Non-Jacobians I: Curves in C (2)

Izadi, Elham

doi:10.1007/s10711-005-9006-3

Cited by 4 publications

(15 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let us briefly explain our methods, similar to [5]. We always assume C to be a smooth nonhyperelliptic curve of genus g 4.…”

Section: E Izadimentioning

confidence: 99%

“…As in [5], for each such translate a , we have a map ν a : H 1 (T A ) −→ H 1 (I Z g−1 ( a )| X ), obtained from Green's exact sequence ([4], see Section 3 below) which factors through the first order obstruction map…”

Section: E Izadimentioning

confidence: 99%

“…The main difference between the method used here and that of [5] is in Sections 5 and 6 below which are more difficult for e > 2 and are where we need some assumptions of genericity on X.…”

Section: E Izadimentioning

confidence: 99%

“…Assume 3 e g − 3 (so g 6), for all e e the curve X e (g 1 d ) is irreducible and reduced and the set of q for which X ∩ Z g−1 = X ∩ Z q has dimension at most g − e − 3. Further suppose that the curve C is nontrigonal and nonbielliptic of genus 7 or nontrigonal of genus 6.…”

Section: E Izadimentioning

confidence: 99%

“…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 other motivations, we refer to the prequel [5] to this paper.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Deforming Curves in Jacobians to Non-Jacobians II: Curves in C(e), 3⩽ e ⩽ g−3*

Izadi

2005

Geom Dedicata

Self Cite

View full text Add to dashboard Cite

We introduce deformation theoretic methods for determining when a curve X in a nonhyperelliptic Jacobian J C will deform with J C to a non-Jacobian. We apply these methods to a particular class of curves in symmetric powers C (e) of C where 3 e g − 3.More precisely, given a pencil g 1 d of degree d on C, let X be the curve parametrizing divisors of degree e in divisors of g 1 d (see the paper for the precise scheme-theoretical definition). Under certain genericity assumptions on the pair (C, g 1 d ), we prove that if X deforms infinitesimally out of the Jacobian locus with J C then either d = 2e, dim H 0 (g 1 d ) = e or d = 2e + 1, dim H 0 (g 1 d ) = e + 1. The analogous result in the case e = 2 without genericity assumptions was proved earlier.

show abstract

“…Let us briefly explain our methods, similar to [5]. We always assume C to be a smooth nonhyperelliptic curve of genus g 4.…”

Section: E Izadimentioning

confidence: 99%

Section: E Izadimentioning

confidence: 99%

“…The main difference between the method used here and that of [5] is in Sections 5 and 6 below which are more difficult for e > 2 and are where we need some assumptions of genericity on X.…”

Section: E Izadimentioning

confidence: 99%

Section: E Izadimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations