# Dan Edidin's Web Page

## Teaching

Math8616, Algebraic Geometry,
MWF 10am, MSB111.

## Research

CV

### 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.