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TITLE Localized Chern characters for 2-periodic complexes
KIAS AUTHORS Kim, Bumsig
JOURNAL SELECTA MATHEMATICA-NEW SERIES, 2022
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ABSTRACT For a two-periodic complex of vector bundles, Polishchuk and Vaintrob have constructed its localized Chem character. We explore some basic properties of this localized Chern character. In particular, we show that the cosection localization defined by Kiem and Li is equivalent to a localized Chern character operation for the associated two-periodic Koszul complex, strengthening a work of Chang, Li, and Li. We apply this equivalence to the comparison of virtual classes of moduli of epsilon-stable quasimaps and moduli of the corresponding LG epsilon-stable quasimaps, in full generality.
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