Intersection of almost complex submanifolds [article]

Weiyi Zhang
2017 arXiv   pre-print
We show the intersection of a compact almost complex subvariety of dimension 4 and a compact almost complex submanifold of codimension 2 is a J-holomorphic curve. This is a generalization of positivity of intersections for J-holomorphic curves in almost complex 4-manifolds to higher dimensions. As an application, we discuss pseudoholomorphic sections of a complex line bundle. We introduce a method to produce J-holomorphic curves using the differential geometry of almost Hermitian manifolds.
more » ... our main result is applied to pseudoholomorphic maps, we prove the singularity subset of a pseudoholomorphic map between almost complex 4-manifolds is J-holomorphic. Building on this, we show degree one pseudoholomorphic maps between almost complex 4-manifolds are actually birational morphisms in pseudoholomorphic category.
arXiv:1707.08253v1 fatcat:7lu47qfkzndh5ijlzb75lxb7ta