Bounds of the number of rational maps between varieties of general type

2005/11/18 by J. C Naranjo, Naranjo, J. C, G. P Pirola +1
Mathematics · #14E05 #14J29 #14J40 #30F30 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14E05 #msc:14J29 #msc:14J40 #msc:30F30

paper · pdf · doi:10.48550/arxiv.math/0511463

21 pages

arxiv created 2005/11/18 · arxiv updated 2009/12/01

Abstract

We give a bound for the number of rational maps between algebraic varieties of general type under mild hypothesis on the canonical map. We use an idea inspired by Tanabe's work. Instead of attaching a morphism of Hodge structures to a rational map we simply associate to it a piece of the integral Hodge lattice. This procedure does not give an injective map, but by means of a geometric argument, we can estimate the number of maps with the same image.

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