Voisin, Claire
Chow ring and gonality of general abelian varieties
Annales Henri Lebesgue, Volume 1 (2018), p. 313-332


KeywordsAbelian varieties, covering gonality, zero-cycles, Chow ring


We study the (covering) gonality of abelian varieties and their orbits of zero-cycles for rational equivalence. We show that any orbit for rational equivalence of zero-cycles of degree k has dimension at most k-1. Building on the work of Pirola, we show that very general abelian varieties of dimension g have (covering) gonality at least f(g), where f(g) grows like log g. This answers a question asked by Bastianelli, De Poi, Ein, Lazarsfeld and B. Ullery. We also obtain results on the Chow ring of very general abelian varieties A of dimension g, e.g., if g2k-1, the set of divisors D Pic 0 (A) such that D k =0 in CH k (A) is at most countable.


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