Rational endomorphisms of Fano hypersurfaces

• Nathan Chen ^[1] ; David Stapleton ^[2]
  1. [1] Stony Brook University

     Stony Brook University

     Town of Brookhaven, Estados Unidos

     
  2. [2] Department of Mathematics, University of California San Diego,USA
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 1, 2024, págs. 2-24
• Idioma: inglés
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• Resumen

  • 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.