The Kodaira Dimension of Lefschetz Fibrations

Abstract

In this note, we verify that the complex Kodaira dimension ${\kappa }^h$ equals the symplectic Kodaira dimension ${\kappa }^s$ for smooth 4-manifolds with complex and symplectic structures. We also calculate the Kodaira dimension for many Lefschetz fibrations.

20 pages, corrected typos and included suggestions made by the referees. To appear in Asian J. of Mathematics

References in corpus (3)

• Wrinkled fibrations on near-symplectic manifolds
• Every 4-Manifold is BLF
• Additivity and Relative Kodaira Dimensions

Cited by in corpus (1)

• Additivity and Relative Kodaira Dimensions