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Poincaré invariants are Seiberg–Witten invariants

Huai-liang Chang and Young-Hoon Kiem
Geometry & Topology 17 (2013) 1149–1163
DOI: 10.2140/gt.2013.17.1149
Abstract

We prove a conjecture of Dürr, Kabanov and Okonek that provides an algebro-geometric theory of Seiberg–Witten invariants for all smooth projective surfaces. Our main technique is the cosection localization principle (Kiem and Li [arXiv:1007.3085]) of virtual cycles.

Keywords
Poincaré invariant, Seiberg–Witten invariants, virtual cycles
Mathematical Subject Classification 2010
Primary: 14J80
References
Publication
Received: 17 October 2012
Revised: 7 November 2012
Accepted: 8 December 2012
Published: 7 May 2013
Proposed: Richard Thomas
Seconded: Jim Bryan, Frances Kirwan
Authors
Huai-liang Chang
Department of Mathematics
Hong Kong University of Science and Technology
Clear Water Bay
Kowloon
Hong Kong
http://www.math.ust.hk/~mahlchang/
Young-Hoon Kiem
Department of Mathematics and Research Institute of Mathematics
Seoul National University
Seoul 151-747
South Korea
http://www.math.snu.ac.kr/~kiem/