Abstract. Given an abelian variety X and a point a ∈ X we denote by < a > the closure of the subgroup of X generated by a. Let N = 2 g − 1. We denote by κ : X → κ(X) ⊂ P N the map from X to its Kummer variety. We prove that an indecomposable abelian variety X is the Jacobian of a curve if and only if there exists a point a = 2b ∈ X \ {0} such that < a > is irreducible and κ(b) is a flex of κ(X).
In this paper we study the algebraic structure of the Tautological ring of a Jacobian: by the use of hard-Lefschetz-primitive classes we construct convenient generators that allow us to list and describe all the possible structures that may occur (the explicit list is given for g ≤ 9 and for a few special curves).
Abstract. We give a new proof of Shiota's theorem on Novikov's conjecture, which states that the K.P. equation characterizes Jacobians among all indecomposable principally polarized abelian varieties.Mathematics Subject Classifications (1991): 14K25, 14H40.
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