Effective characterization of quasi-abelian surfaces

TL;DR

This paper proves that for certain smooth quasi-projective surfaces with specific logarithmic invariants, the quasi-Albanese morphism is birational and proper outside a finite set, refining a classical Iitaka result.

Contribution

It provides a sharp effective version of Iitaka's classical theorem for quasi-abelian surfaces with specified logarithmic invariants.

Findings

Quasi-Albanese morphism is birational for the given surfaces.

Existence of a finite set where the map is proper.

Refinement of classical Iitaka theorem.

Abstract

Let V be a smooth quasi-projective complex surface such that the three first logarithmic plurigenera are equal to 1 and the logarithmic irregularity is equal to 2. We prove that the quasi-Albanese morphism of V is birational and there exists a finite set S such that the quasi-Albanese map is proper over the complement of S in the quasi-Albanese variety A(V) of V. This is a sharp effective version of a classical result of Iitaka.