Endomorphisms of hypersurfaces of Fano manifolds of Picard number 1

2009/07/21 by Insong Choe, Choe, Insong
Mathematics · #14J70 #14M20 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14J70 #msc:14M20

paper · pdf · doi:10.48550/arxiv.0907.3547

to appear in Mathematische Nachrichten

arxiv created 2009/07/21 · arxiv updated 2009/12/01

Abstract

It is conjectured that a Fano manifold of Picard number 1 which is not a projective space admits no endomorphisms of degree bigger than 1. Beauville confirmed this for hypersurfaces of projective space. We study this problem for hypersurfaces of an arbitrary Fano manifold of Picard number 1.

Related

• Fano Varieties with Large Degree Endomorphisms
• Fano manifolds of Picard number one whose co-tangent bundle is algebraically completely integrable system and its endomorphisms
• Endomorphisms of hypersurfaces and other manifolds
• Endomorphisms of projective varieties
• Fano manifolds obtained by blowing up along curves with maximal Picard number