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

Autor:	Bonthrone, Louis, Zhang, Weiyi
Rok vydání:	2018
Předmět:	Mathematics - Differential Geometry Mathematics - Symplectic Geometry
Druh dokumentu:	Working Paper
Popis:	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. Comment: 28 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1808.09356 Zobrazit plný text záznamu View this record from Arxiv