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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Localizing virtual cycles by cosections


Authors: Young-Hoon Kiem and Jun Li
Journal: J. Amer. Math. Soc. 26 (2013), 1025-1050
MSC (2010): Primary 14N35
Published electronically: March 27, 2013
MathSciNet review: 3073883
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Abstract: We show that a cosection of the obstruction sheaf of a perfect obstruction theory localizes the virtual cycle to the non-surjective locus of the cosection. We construct a localized Gysin map and localized virtual cycles. Various applications of this construction are discussed.


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Additional Information

Young-Hoon Kiem
Affiliation: Department of Mathematics and Research Institute of Mathematics, Seoul National University, Seoul 151-747, Korea
Email: kiem@math.snu.ac.kr

Jun Li
Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305
Email: jli@math.stanford.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-2013-00768-7
PII: S 0894-0347(2013)00768-7
Received by editor(s): February 11, 2011
Received by editor(s) in revised form: November 28, 2012
Published electronically: March 27, 2013
Additional Notes: The first author was partially supported by NRF grant 2011-0027969
The second author was partially supported by NSF grant NSF-0601002
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.