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arXiv · alg-geom/9309001

Theoremes de connexites et varietes abeliennes

Olivier Debarre
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Abstract

We prove a connexity theorem for abelian varieties in characteristic $0$: if $X$ is an abelian variety and $V\rightarrow X$ and $W\rightarrow X$ two morphisms, then, under certain hypotheses, the fiber product of $V$ and $W$ over $X$ is connected. This theorem has several consequences: the algebraic fundamental groups of a simple abelian variety $X$ and of a normal subvariety $V$ of $X$ of dimension $> dim(X)/2$ are isomorphic. The same holds when $V$ is a finite cover of degree $\le dim(X)$ of $X$. (The only difference between this replacement and the original submission is that one of the conjectures is now proved).

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Olivier Debarre. 1993-09-21. Theoremes de connexites et varietes abeliennes. https://arxiv.org/abs/alg-geom/9309001

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