Let V be a smooth quasi-projective complex surface such that the first three logarithmic plurigenera P-1(V) , P-2(V) and P-3(V) are equal to 1 and the logarithmic irregularity q(V) is equal to 2. We prove that the quasi-Albanese morphism a(v): V -> A(V) is birational and there exists a finite set S such that a(v) is proper over A(V) \ S , thus giving a sharp effective version of a classical result of Iitaka [12].
Effective characterization of quasi-abelian surfaces
Mendes Lopes M.;Pardini R.;Tirabassi S.
2023-01-01
Abstract
Let V be a smooth quasi-projective complex surface such that the first three logarithmic plurigenera P-1(V) , P-2(V) and P-3(V) are equal to 1 and the logarithmic irregularity q(V) is equal to 2. We prove that the quasi-Albanese morphism a(v): V -> A(V) is birational and there exists a finite set S such that a(v) is proper over A(V) \ S , thus giving a sharp effective version of a classical result of Iitaka [12].File in questo prodotto:
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