Complex projective nonruled surfaces S endowed with a numerically effective line bundle L of arithmetic genus g(S,L)=2 are investigated. In view of existing results on elliptic surfaces we focus on surfaces of Kodaira dimension k(S)=0 and 2. Structure results are provided in both cases according to the values of L^2. When S is not minimal we describe explicitly the structure of any birational morphism from S to its minimal model S', reducing the study of (S,L) to that of (S',L'), where L' is a numerically effective line bundle with g(S',L')=2 or 3. Our description of (S,L) when S is minimal, as well as that of the pair (S',L') when g(S',L')=3 relies on on several results concerning linear systems, mainly on surfaces of Kodaira dimension zero. Moreover, several examples are provided, especially to enlighten the case in which S is a minimal surface of general type, (S,L) having Iitaka dimension 1.

Semipolarized nonruled surfaces with sectional genus two / A. Biancofiore, M.L. Fania, A. Lanteri. - In: BEITRAGE ZUR ALGEBRA UND GEOMETRIE. - ISSN 0138-4821. - 47:1(2006), pp. 175-193.

Semipolarized nonruled surfaces with sectional genus two

A. Lanteri
Ultimo
2006

Abstract

Complex projective nonruled surfaces S endowed with a numerically effective line bundle L of arithmetic genus g(S,L)=2 are investigated. In view of existing results on elliptic surfaces we focus on surfaces of Kodaira dimension k(S)=0 and 2. Structure results are provided in both cases according to the values of L^2. When S is not minimal we describe explicitly the structure of any birational morphism from S to its minimal model S', reducing the study of (S,L) to that of (S',L'), where L' is a numerically effective line bundle with g(S',L')=2 or 3. Our description of (S,L) when S is minimal, as well as that of the pair (S',L') when g(S',L')=3 relies on on several results concerning linear systems, mainly on surfaces of Kodaira dimension zero. Moreover, several examples are provided, especially to enlighten the case in which S is a minimal surface of general type, (S,L) having Iitaka dimension 1.
smooth complex projective surfaces, nef line bundles, sectional genus.
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/8592
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