Localized Chern characters for 2-periodic complexes

• Bumsig Kim ^[1] ; Jeongseok Oh ^[2]
  1. [1] Korea Institute for Advanced Study

     Korea Institute for Advanced Study

     Corea del Sur

     
  2. [2] Imperial College, Reino Unido
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 2, 2022
• Idioma: inglés
• Enlaces
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• Resumen

  • For a two-periodic complex of vector bundles, Polishchuk and Vaintrob have constructed its localized Chern 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 ε-stable quasimaps and moduli of the corresponding LG ε-stable quasimaps, in full generality.