Localizing virtual cycles by cosections

Kiem, Young-Hoon; Li, Jun

doi:10.1090/S0894-0347-2013-00768-7

Localizing virtual cycles by cosections
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by Young-Hoon Kiem and Jun Li

J. Amer. Math. Soc. 26 (2013), 1025-1050

DOI: https://doi.org/10.1090/S0894-0347-2013-00768-7

Published electronically: March 27, 2013

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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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