Fano Varieties with Large Degree Endomorphisms

2009/01/13 by Janós Kollár, Chenyang Xu, Kollár, János +1 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Meromorphic and Entire Functions #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0901.1692

Abstract

We give examples of Fano varieties X with Picard number 1, which have terminal singularities and admit endomorphisms with degree larger than 1.

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• Symmetric power of higher dimensional varieties

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• Endomorphisms of hypersurfaces of Fano manifolds of Picard number 1
• Fano varieties with high degree
• Fano varieties with conjecturally largest Fano index
• Fano varieties with Nef(X)=Psef(X) and ρ(X)=dim X-1
• Endomorphisms of varieties and Bott vanishing