On rational maps from a general surface in P³ to surfaces of general type

2006/11/01 by Guerra, Lucio, Pirola, Gian Pietro
#14E05 #14J29 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0611026

Abstract

We study the dominant rational maps from a general surface in P³ to surfaces of general type. We prove restrictions on the target surfaces, and special properties of the rational maps. We show that for a small degree the general surface has no such map. Moreover a slight improvement of a result of Catanese, on the number of moduli of a surface of general type, is also obtained.

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• Restrictions on rational surfaces lying in very general hypersurfaces
• On rational maps from the product of two general curves