Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Dr. Yuhang Chen, Ohio State University
Inviter:	Prof. Baohua Fu
Title:	ORBIFOLD HIRZEBRUCH-RIEMANN-ROCH
Language:	Chinese
Time & Venue:	2023.06.13 15:30-16:30 MCM410
Abstract:	This talk is mainly expository with the purpose of demystifying the Riemann-Roch theorem for Deligne-Mumford (DM) stacks. In this talk, I will restrict DM stacks to quotient stacks. I will review some basic facts about the K-theory of quotient stacks and derive an orbifold Hirzebruch Riemann-Roch (HRR) formula for connected proper smooth quotient stacks. Let X be a connected separated quotient stack. I will study the inertia stack IX of X in details. In particular, we will decompose IX into connected components. Such a decomposition is essential in the constructions of the orbifold Chern character e ch(E) and the orbifold Todd class e td(E) of a coherent sheaf E on X when X is smooth. I will derive explicit formulas for e ch(E) and e td(E). I will define an orbifold Mukai pairing and derive an orbifold HRR formula for X when it is proper and smooth. I will show that the orbifold HRR formula for the classifying stack BG when G=Z/nZ recovers Parseval’s theorem for the discrete Fourier transform.