Zhang, Weiyi (2021) Moduli space of J-holomorphic subvarieties. Selecta Mathematica, New Series, 27 (2). 29. doi:10.1007/s00029-021-00648-z ISSN 1022-1824.

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Abstract

We study the moduli space of J-holomorphic subvarieties in a 4-dimensional symplectic manifold. For an arbitrary tamed almost complex structure, we show that the moduli space of a sphere class is formed by a family of linear system structures as in algebraic geometry. Among the applications, we show various uniqueness results of J-holomorphic subvarieties, e.g. for the fiber and exceptional classes in irrational ruled surfaces. On the other hand, non-uniqueness and other exotic phenomena of subvarieties in complex rational surfaces are explored. In particular, connected subvarieties in an exceptional class with higher genus components are constructed. The moduli space of tori is also discussed, and leads to an extension of the elliptic curve theory.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Moduli theory, Analytic spaces, Geometry, Algebraic
Journal or Publication Title:	Selecta Mathematica, New Series
Publisher:	Birkhauser Verlag AG
ISSN:	1022-1824
Official Date:	28 April 2021
Dates:	Date Event 28 April 2021 Published 21 April 2021 Accepted
Volume:	27
Number:	2
Article Number:	29
DOI:	10.1007/s00029-021-00648-z
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)
Date of first compliant deposit:	4 May 2021
Date of first compliant Open Access:	4 May 2021

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