Communications in Analysis and Geometry
Volume 30 (2022)
$J$-holomorphic curves from closed $J$-anti-invariant forms
Pages: 1196 – 1226
We study the relation between $J$-anti-invariant $2$-forms and pseudo-holomorphic 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.
Received 28 February 2019
Accepted 9 January 2020
Published 26 April 2023