New Series: Moduli of Riemann Surfaces

Though I’m not quite ready to start (next week!) I feel that, in the spirit of Jim getting back to the blogging and my continued promises, I’d announce my series now.  I’m going to start a detailed series on the moduli of Riemann surfaces, including both topological and geometric aspects.  And I figured I’d start it out with a list of references for some of the topics that I’d be covering:

Books

Algebraic Curves and Riemann Surfaces by Miranda
Geometry of Algebraic Curves Volumes I and II
  by Arbarello, Cornalba, Griffiths and Harris
Geometric Invariant Theory by Mumford, Fogarty and Kirwan
Lectures on Curves on an Algebraic Surface by Mumford
Principles of Algebraic Geometry by Griffiths and Harris
Rational Curves on Algebraic Varieties by Kollár
Moduli of Curves by Harris and Morrison

Papers

“Complete subvarieties of the moduli space of smooth curves” by Diaz
“Curves and their moduli” by Harris
“Algorithms for computing intersection numbers on the moduli space of curves, with an application to the class of hte locus of Jacobians” by Faber
“The structure of the moduli spaces of curves and abelian varieties” by Mumford
“On the Kodaira dimension of the moduli space of curves” by Mumford
“Picard groups of moduli problems” by Mumford
“The irreducibility fo the space of curves of a given genus” by Deligne and Mumford
“The projectivity of the moduli space of stable curves I: Preliminaries on “det” and “Div” ” by Knudsen and Mumford
The projectivity of the moduli space of stable curves. II. The stacks M_{g,n}” by Knudsen
“The projectivity of the moduli space of stable curves. III. The line bundles on M_{g,n}, and a proof of the projectivity of \overline{M}_{g,n} in characteristic 0.” by Knudsen
“The Picard groups of the moduli spaces of curves” by Arbarello and Cornalba
“The second homology group of the mapping class group of an orientable surface” by Harer
“The virtual cohomological dimension of the mapping class group of an orientable surface” by Harer
“Divisors in the moduli spaces of curves” by Arbarello and Cornalba
“Teichmüller space via Kuranishi families” by Arbarello and Cornalba

From Moduli Spaces of Riemann Surfaces edited by Farb, Hain and Looijenga:
“Teichmüller Theory” by Hamenstädt
“The Mumford Conjecture, Madsen-Weiss and Homological Stability for Mapping Class Groups of Surfaces” by Wahl
“Lectures on the Madsen-Weiss Theorem” by Galatius
“Tautological Algebras of Moduli Spaces of Curves” by Faber

I’ll update this list when new references are introduced, should I do so.

About Charles Siegel

Charles Siegel is currently a postdoc at Kavli IPMU in Japan. He works on the geometry of the moduli space of curves.
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