Resumen de Rational endomorphisms of Fano hypersurfaces

Nathan Chen, David Stapleton

• 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 ≥ 5(n +3)/6 are not birational to Jacobian fibrations of dimension one. A key part of the argument is to resolve singularities of general μp-covers in mixed characteristic p.