Department Seminars & Colloquia
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We give some constructions of a rational curve in the quotients of abelian varieties by finite groups. And we talk about the growth of the rank of abelian varieties as its application.
The most recent related result which is a joint work with Michael Larsen is the following : For an abelian variety $A$ and a finite group $G$ of automorphisms of $A$, if $G$ contains an element whose action on $Lie(A)$ has an invariant subspace of codimension $2$, we show that the quotient $A/G$ contains a uniruled hypersurface.