In this paper, we study birational immersions from a very general smooth plane curve to a nonrational surface with pg =q =0 to treat dominant rational maps from a very general surface X of degree ≥ 5 in 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.
On Subfields of the Function Field of a General Surface in ℙ3
Pirola G. P.
2015-01-01
Abstract
In this paper, we study birational immersions from a very general smooth plane curve to a nonrational surface with pg =q =0 to treat dominant rational maps from a very general surface X of degree ≥ 5 in 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.File in questo prodotto:
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