Gonality and zero-cycles of abelian varieties
Also appears in collection : French-German meeting on complex algebraic geometry / Rencontre franco-allemande en géométrie algébrique complexe
The gonality of a variety is defined as the minimal gonality of curve sitting in the variety. We prove that the gonality of a very general abelian variety of dimension $g$ goes to infinity with $g$. We use for this a (straightforward) generalization of a method due to Pirola that we will describe. The method also leads to a number of other applications concerning $0$-cycles modulo rational equivalence on very general abelian varieties.
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