Poincaré invariants are Seiberg–Witten invariants

Chang, Huai-liang; Kiem, Young-Hoon

doi:10.2140/gt.2013.17.1149

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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/

Volume 17, issue 2 (2013)