Seiberg–Witten and Gromov invariants for
self-dual harmonic 2–forms

Gerig, Chris

doi:10.2140/gt.2022.26.3307

Geom. Topol.

2022

DOI: 10.2140/gt.2022.26.3307

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Seiberg–Witten and Gromov invariants for self-dual harmonic 2–forms

Chris Gerig

Abstract: Seiberg-Witten and Gromov invariants for self-dual harmonic 2-forms

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

Bonthrone

Zhang

2022

Communications in Analysis and Geometry

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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 2forms 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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$J$-holomorphic curves from closed $J$-anti-invariant forms

Bonthrone

Zhang

2022

Communications in Analysis and Geometry

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Seiberg–Witten and Gromov invariants for self-dual harmonic 2–forms

Abstract: Seiberg-Witten and Gromov invariants for self-dual harmonic 2-forms

Cited by 1 publication

References 64 publications

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

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

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