On subfields of the function field of a general surface in \mathbb P³

2014/09/03 by Yongnam Lee, Gian Pietro Pirola, Lee, Yongnam +1
Mathematics · #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1409.1097

Abstract

In this paper we study birational immersions from a very general smooth plane curve to a non-rational surface with p_g=q=0 to treat dominant rational maps from a very general surface X of degree≥ 5 in \mathbb P³ to smooth projective surfaces Y. Based on the classification theory of algebraic surfaces, Hodge theory, and deformation theory, we prove that there is no dominant rational map from X to Y unless Y is rational or Y is birational to X.

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