Rational endomorphisms of Fano hypersurfaces

Nathan Chen; David Stapleton

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arXiv · 2103.12207

Rational endomorphisms of Fano hypersurfaces

Nathan Chen·David Stapleton

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Abstract

We show that the degrees of rational endomorphisms of very general complex Fano and Calabi-Yau hypersurfaces satisfy certain congruence conditions by specializing to characteristic p. As a corollary we show that very general n-dimensional hypersurfaces of degree $d\ge 5\lceil (n+3)/6\rceil$ are not birational to elliptic fibrations. A key part of the argument is to resolve singularities of general p-cyclic covers in mixed characteristic p.

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Nathan Chen, David Stapleton. 2021-03-22. Rational endomorphisms of Fano hypersurfaces. https://arxiv.org/abs/2103.12207

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