  Title: Indecomposable Higher Chow Cycles on Low Dimensional Jacobians
Authors: Alberto Collino Comments: AMS-TeX, 10 pages Subj-class: Algebraic
Geometry MSC-class: 14C30 ;19E15 There is a basic indecomposable higher cycle K
in Bloch's higher Chow group CH^{g}(J(C),1) on the Jacobian J(C) of a general
hyperelliptic curve C of genus g. Consider K(t) the translation of K associated
with a point t in C, we prove that in general K - K(t) is indecomposable if the
genus is at least 3. Our tool is Lewis' condition for indecomposability. We
show next that on the jacobian J(C) of a general curve C of genus 3 there is a
geometrically natural family of higher cycles, when C becomes hyperelliptic the
family in the limit contains a component of indecomposable cycles of type K -
K(t).
