## Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: The geometry of moduli spaces of curves

Seminar | September 11 | 3:45-4:45 p.m. | 939 Evans Hall

Brian Osserman, UC Davis

Department of Mathematics

In this expository talk, we discuss from an elementary point of view how one approaches studying the geometry of moduli spaces of curves. We begin with classical examples of how one can prove that some moduli spaces are unirational. At the opposite extreme, following ideas of Harris, Mumford, Eisenbud and Farkas, we then explain how one can reduce proving that moduli spaces are of general type to the study of carefully chosen effective divisors on them.

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