Localization by 2-periodic complexes and virtual structure sheaves

TL;DR

This paper develops a K-theoretic analogue of localized Chern characters for 2-periodic complexes and applies it to compare virtual structure sheaves in moduli spaces of stable quasimaps and LG-quasimaps.

Contribution

It introduces a K-theoretic version of the localized Chern character map and demonstrates its equivalence to the cosection localized Gysin map for Koszul 2-periodic complexes.

Findings

K-theoretic localized Chern character coincides with cosection localized Gysin map for Koszul complexes.

Comparison of virtual structure sheaves of moduli spaces of stable quasimaps and LG-quasimaps.

Extension of localized Chern character techniques to K-theory context.

Abstract

B. Kim and the first author proved a result comparing the virtual fundamental classes of the moduli spaces of stable quasimaps and 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 by Y.-H. Kiem and J. Li. As an application we compare the virtual structure sheaves of the moduli space of stable quasimaps and stable LG-quasimaps.