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- W2737921102 abstract "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. When 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." @default.
- W2737921102 created "2017-07-31" @default.
- W2737921102 creator A5058215602 @default.
- W2737921102 date "2017-07-25" @default.
- W2737921102 modified "2023-09-27" @default.
- W2737921102 title "Intersection of almost complex submanifolds" @default.
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- W2737921102 doi "https://doi.org/10.48550/arxiv.1707.08253" @default.
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