Additivity and Relative Kodaira Dimensions

Abstract

In this paper we introduce the notion of relative Kodaira dimension for a symplectic 4-manifold M with a possibly disconnected embedded symplectic surface F. One notable feature is that the sphere components of F have to be discarded, which resembles the definition of Thurston norm of 3-manifolds. To define it we need to establish several homological properties of embedded symplectic surfaces. We also formulate the notion of relative minimal model, and prove the existence and the somewhat surprising uniqueness.

33 pages; dedicated to Shing-Tung Yau on the occasion of his 60th birthday

References in corpus (7)

• Algebraic surfaces and Seiberg-Witten invariants
• A simply connected surface of general type with p_g=0 and K^2=2
• Lefschetz pencils and divisors in moduli space
• A simply connected surface of general type with p_g=0 and K^2=4
• Iitaka conjecture $C_{n,m}$ in dimension six
• The Relative Symplectic Cone and T^2-Fibrations
• The Kodaira Dimension of Lefschetz Fibrations

Cited by in corpus (5)

• Kodaira dimensions of almost complex manifolds II
• Circular spherical divisors and their contact topology
• Relative Ruan and Gromov-Taubes Invariants of Symplectic 4-Manifolds
• The Kodaira Dimension of Lefschetz Fibrations
• Symplectic isotopy on non-minimal ruled surfaces