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$J$-holomorphic curves from closed $J$-anti-invariant forms

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arxiv 1808.09356 v2 pith:2I7KDJ5J submitted 2018-08-28 math.DG math.SG

Louis Bonthrone , Weiyi Zhang This is my paper · ORCID
classification math.DGmath.SG
keywords anti-invariantclosedformsalmostcomplexcurvesholomorphicinvariant
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abstract

We study the relation between $J$-anti-invariant $2$-forms and pseudoholomorphic curves in this paper. We show the zero set of a closed $J$-anti-invariant $2$-form on an almost complex $4$-manifold supports a $J$-holomorphic subvariety in the canonical class. This confirms a conjecture of Draghici-Li-Zhang. A higher dimensional analogue is established. We also show the dimension of closed $J$-anti-invariant $2$-forms on an almost complex $4$-manifold is a birational invariant, in the sense that it is invariant under degree one pseudoholomorphic maps.

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  1. On the Anti-Invariant Cohomology of Almost Complex Manifolds

    math.DG 2019-08 accept novelty 7.0 of 10

    New explicit almost complex structures show that closed anti-invariant 2-forms range from infinite-dimensional to zero-dimensional on R^4, and produce compact examples with maximal or arbitrarily large anti-invariant ...

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