# Mathematical Sciences Research Institute

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# Seminar

Geometry of Hurwitz Spaces March 18, 2013 (04:10 PM PDT - 05:00 PM PDT)
Location: UC Berkeley, 60 Evans Hall
Speaker(s) Joe Harris
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Abstract/Media

Riemann surfaces, which we now think of abstractly as smooth algebraic
curves over the complex numbers, were described by Riemann as graphs of
multivalued holomorphic functions-in other words, branched covers of the
Riemann sphere $\P^1$. The Hurwitz spaces, varieties parametrizing the
set of branched covers of $\P^1$ of given degree and genus, are still
central objects in the study of curves and their moduli. In this talk, we'll
describe the geometry of Hurwitz spaces and their compactifications, leading
up to recent work of Anand Patel and others.

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