Non representability of twice the minimal class in a generic Jacobian
type: Item
instance of: scholarly article
title: Non representability of twice the minimal class in a generic Jacobian
zbMATH Open document ID: 0803.14014
DOI: 10.1007/BF01189574
published in: Archiv der Mathematik
publication date: 1994-11-13T00:00:00Z
review text: Let \(A\) be a principally polarized abelian variety of dimension \(a\), and let \(\Theta\) be a divisor representing the polarization. We shall say \(A\) is \(m\)-representable, for an integer \(m\), if there exists an integral curve \(C \subset A\) with cohomological class \(m \cdot {[\Theta]^{a - 1} \over (a - 1)!}\). For example, \(A\) is the Jacobian of a curve if and only if \(A\) is 1-representable (Matsusaka's theorem). In this paper we prove that a generic Jacobian of dimension \(\geq 6\) is not 2-representable.
Mathematics Subject Classification ID: 14H40
Mathematics Subject Classification ID: 14K05
zbMATH DE Number: 687032
zbMATH Keywords: \(m\)-representable principally polarized abelian variety
zbMATH Keywords: Jacobian
author: Juan Carlos Naranjo
MaRDI profile type: Publication
cites work: Curves of genus \(g\) lying on a \(g\)-dimensional Jacobian variety
cites work: On a characterization of a Jacobian variety
cites work: Q4053768
cites work: Q4112043
cites work: Q3786562
full work available at URL: https://doi.org/10.1007/bf01189574
OpenAlex ID: W2010563349
description: scientific article; zbMATH DE number 687032