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LOCALIZATION BY $2$-PERIODIC COMPLEXES AND VIRTUAL STRUCTURE SHEAVES

Part of: Cycles and subschemes Projective and enumerative geometry

Published online by Cambridge University Press:  22 December 2020

Jeongseok Oh  and
Bhamidi Sreedhar Open the ORCID record for Bhamidi Sreedhar [Opens in a new window]
Jeongseok Oh
Affiliation:
School of Mathematics, Korea Institute for Advanced Study (KIAS), 85 Hoegi-ro, Dongdaemun-gu, Seoul02455, Republic of Korea (jeongseok@kias.re.kr, sreedhar@kias.re.kr)
Bhamidi Sreedhar
Affiliation:
School of Mathematics, Korea Institute for Advanced Study (KIAS), 85 Hoegi-ro, Dongdaemun-gu, Seoul02455, Republic of Korea (jeongseok@kias.re.kr, sreedhar@kias.re.kr)
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Abstract

In [12], Kim and the first author proved a result comparing the virtual fundamental classes of the moduli spaces of $\varepsilon $ -stable quasimaps and $\varepsilon $ -stable $LG$ -quasimaps by studying localized Chern characters for $2$ -periodic complexes.

In this paper, we study a K-theoretic analogue of the localized Chern character map and show that for a Koszul $2$ -periodic complex it coincides with the cosection-localized Gysin map of Kiem and Li [11]. As an application, we compare the virtual structure sheaves of the moduli space of $\varepsilon $ -stable quasimaps and $\varepsilon $ -stable $LG$ -quasimaps.

Keywords

virtual structure sheavesmoduli spaces

MSC classification

Primary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants
Secondary: 14C35: Applications of methods of algebraic $K$-theory
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 21 , Issue 5 , September 2022 , pp. 1477 - 1506
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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