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

2018/08/28 by Bonthrone, Louis, Zhang, Weiyi
#Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1808.09356

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.

Related

• Intersection of almost complex submanifolds
• Estimates for J-curves as submanifolds
• On the Anti-Invariant Cohomology of Almost Complex Manifolds
• On the J-anti-invariant cohomology of almost complex 4-manifolds
• J-holomorphic curves in a nef class