Dan Edidin's Web Page


Math8616, Algebraic Geometry, MWF 10am, MSB111.



Recent Papers

Toward a mathematical theory of the crystallographic phase retrieval problem, with Tamir Bendory https://arxiv.org/abs/2002.10081

The cone theorem and the vanishing of Chow cohomology, with Ryan Richey, to appear in the Proceedings of the Facets in Algebraic Geometry conference in honor of William Fulton's 80th birthday. https://arxiv.org/abs/2002.00083

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.