\(J\)-holomorphic curves from closed \(J\)-anti-invariant forms

DOI10.4310/CAG.2022.V30.N6.A1zbMATH Open1521.32031arXiv1808.09356MaRDI QIDQ6043433

Author name not available (Why is that?)

Publication date: 5 May 2023

Published in: Communications in Analysis and Geometry (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1808.09356

zbMATH Keywords

almost complex manifoldspseudoholomorphic curves

Mathematics Subject Classification ID

Almost complex manifolds (32Q60) Pseudoholomorphic curves (32Q65)

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