Algebra and Geometry Seminar

The localized Chern character of a bounded complex of vector bundles is a bivariant class defined by Baum, Fulton, and MacPherson. They used such classes to prove the general Riemann-Roch theorem for singular varieties. For a two-periodic complex of vector bundles, Polishchuk and Vaintrob have constructed its localized Chern character, which is a generalization of the usual one. We discuss some properties of PV's localized Chern characters. In particular, cosection localizations defined by Kiem and Li can be expressed as these localized Chern character operations. This result is a generalization of the related work by Chang, Li, and Li. The talk is based on joint work with Bumsig Kim.