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arXiv · 1409.1097

On subfields of the function field of a general surface in ${\mathbb P}^3$

Yongnam Lee·Gian Pietro Pirola
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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$\geq 5$ in ${\mathbb P}^3$ 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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Yongnam Lee, Gian Pietro Pirola. 2014-09-03. On subfields of the function field of a general surface in ${\mathbb P}^3$. https://arxiv.org/abs/1409.1097

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