A plethora of inertial products
Abstract
For a smooth Deligne-Mumford stack X we describe a large number of inertial products on K(IX) and A*(IX) and corresponding inertial Chern characters. We do this by developing a theory of inertial pairs. Each inertial pair determines an inertial product on K(IX) and an inertial product on A*(IX) and Chern character ring homomorphisms between them. We show that there are many inertial pairs; indeed, every vector bundle V on X defines two new inertial pairs. We recover, as special cases, the orbifold products of Chen-Run, Abramovich-Graber-Vistoli, Jarvis-Kaufmann-Kimura, and Edidin-Jarvis-Kimura and the virtual product of Gonzalez-Lupercio-Segovia-Uribe-Xicotencatl. We also introduce an entirely new product we call the localized orbifold product, which is defined on the complexification of K(IX). The inertial products developed in this paper are used in a subsequent paper to describe a theory of inertial Chern classes and power operations in inertial K-theory. These constructions provide new manifestations of mirror symmetry, in the spirit of the Hyper-Kaehler Resolution Conjecture.
Keywords
Cite
@article{arxiv.1209.2068,
title = {A plethora of inertial products},
author = {Dan Edidin and Tyler J. Jarvis and Takashi Kimura},
journal= {arXiv preprint arXiv:1209.2068},
year = {2016}
}
Comments
20 pages. Several minor errors corrected. To appear in Annals of K-Theory