General curves on algebraic surfaces
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Edoardo Sernesi
Abstract
We give upper bounds on the genus of a curve with general moduli assuming that it can be embedded in a projective nonsingular surface Y so that dim(|C|) > 0. We find such bounds for all types of surfaces of intermediate Kodaira dimension and, under mild restrictions, for surfaces of general type whose minimal model Z satisfies the Castelnuovo inequality KZ2 ≥ 3χ(𝒪Z) - 10. In this last case we obtain g ≤ 19. In the other cases considered the bounds are lower.
Funding source: GNSAGA-INDAM
Funding source: 2008 PRIN
Award Identifier / Grant number: Geometria delle varietà algebriche e loro spazi di moduli
I thank E. Ballico, L. Benzo, A. Bruno, F. Catanese, C. Ciliberto, A. Lopez, M. Reid, M. Roth and A. Verra for useful conversations related to this work. Remarks and questions of the referee contributed to improve the paper significantly. I am very thankful to him.
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- Geometric analysis aspects of infinite semiplanar graphs with nonnegative curvature
- Rigidity and stability of Einstein metrics for quadratic curvature functionals
- On the Morse–Sard property and level sets of Wn,1 Sobolev functions on ℝn
- Hecke algebras associated to Λ-adic modular forms
- On a notion of exactness for reduced free products of C*-algebras
- Splitting theorems for Finsler manifolds of nonnegative Ricci curvature
- Weil–Châtelet divisible elements in Tate–Shafarevich groups II: On a question of Cassels
- General curves on algebraic surfaces
- Operator biflatness of the L1-algebras of compact quantum groups
Articles in the same Issue
- Frontmatter
- Geometric analysis aspects of infinite semiplanar graphs with nonnegative curvature
- Rigidity and stability of Einstein metrics for quadratic curvature functionals
- On the Morse–Sard property and level sets of Wn,1 Sobolev functions on ℝn
- Hecke algebras associated to Λ-adic modular forms
- On a notion of exactness for reduced free products of C*-algebras
- Splitting theorems for Finsler manifolds of nonnegative Ricci curvature
- Weil–Châtelet divisible elements in Tate–Shafarevich groups II: On a question of Cassels
- General curves on algebraic surfaces
- Operator biflatness of the L1-algebras of compact quantum groups
