2015/01/27 by Weiyi Zhang, Zhang, Weiyi · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1501.06744
openalex publication_date 2015/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study the curve cone of an almost complex 4-manifold which is tamed by a symplectic form. In particular, we prove the cone theorem as in Mori theory for all such manifolds using the Seiberg-Witten theory. For small rational surfaces and minimal ruled surfaces, we study the configuration of negative curves. We define abstract configuration of negative curves, which records the homological and intersection information of curves. Combinatorial blowdown is the main tool to study these configurations. As an application of our investigation of the curve cone, we prove the Nakai-Moishezon type duality for all almost Kähler structures on \mathbb CP2#k\mathbb CP2 with k≤ 9 and minimal ruled surfaces with a negative curve. This is proved using a version of Gram-Schmidt orthogonalization process for the J-tamed symplectic inflation.