Dan Edidin's Web Page

I-70 Algebraic Geometry Symposium, November 11-12, 2017, University of Kansas

Math 4920/7290 Fall 2017

Lecture Notes on Equivariant Algebraic Geometry


Research

CV

Recent Papers

Canonical Reduction of stabilizers for Artin stacks with good moduli spaces (with David Rydh) (arxiv:1710.03220)

Towards an intersection Chow cohomology for GIT quotients (with Matt Satriano) (arxiv:1707.05890)

On Signal reconstruction from FROG measurements (with Tamir Bendory and Yonina Eldar) (arxiv:1706.08494)

Inertial Chow rings of toric stacks  (with Thomas Coleman), Manuscripta Math, to appear   (arxiv:1612:07107)

Strong cycles and intersection products on good moduli spaces  (with Matt Satriano) to appear in the Proceedings of the  2016 Interntational Colloquium on K-theory, Tata Institute  (arxiv:1609.08162)

Chern classes and compatible power operations in inertial K-theory (with Tyler Jarvis and Takashi Kimura), Annals of K-theory, volume 2, no 1, 73--130 (2017).

Projections and Phase retrieval, Applied and Computational Harmonic Analysis, 42,  no 2, 350--359 (2017).

Strong regular embeddings of Deligne-Mumford stacks and hypertoric geometry  Michigan Journal of Math 65, no 2, 389--412 (2016)   (arxiv:1503.04828)

A plethora of inertial products  (with Tyler Jarvis and Takashi Kimura)  Annals of K-theory vol 1, no 1, 85--108 (2016).


Papers on Stacks


Notes on the construction of the moduli space of curves
An introduction to stacks from the point of view of moduli of curves. This article appeared in the Proceedings of the 1997 Bologna Conference on Intersection Theory (G. Ellingsrud, W. Fulton, S. Kleiman and A. Vistoli, eds.), Birkhauser (2000).

Characterization of Deligne-Mumford stacks
A detailed corrected proof of Theorem 2.1 of "Notes on the construction of the moduli space of curves", characterizing DM stacks as those stacks which have unramified diagonal and a smooth cover by a scheme. Another proof appears in the book "Champs algebriques" by Laumon and Moret-Bailly (Theorem 8.1).

What is a stack?
This very brief introduction appeared in the "What is..." column of the Notices of the AMS, April 2003.

Equivariant algebraic geometry and the cohomology of the moduli space of curves

In this expository article we give a functorial definition of the integral cohomology ring of a stack. We show that for quotient stacks this cohomology can  be identified with equivariant cohomology. Our focus is on the stacks of smooth and stable curves. This will appear in the forthcoming Handbook of Moduli edited by G. Farkas and I. Morrison.

Riemann-Roch for Deligne-Mumford stacks
We give a simple proof of the Riemann-Roch theorem for Deligne-Mumford stacks using the equivariant Riemann-Roch theorem and the localization theorem in equivariant K-theory together with some basic commutative algebra of Artin rings. This will appear in the Proceedings of the Joe Harris 60th Birthday Conference.

There is no degree map for 0-cycles on Artin stacks (with Anton Geraschenko and Matthew Satriano)
We show that there is no way to define degrees of 0-cycles on Artin stacks with proper good moduli spaces so that (i) the degree of an ordinary point is non-zero and (ii) degrees are compatible with closed immersions.