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School on birational geometry and moduli spaces
June 1-11, 2010 at the University of Utah |
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Speakers Schedule Application Contact MRC 2010- Snowbird Home |
Renzo Cavalieri, June 1 - June 4, 10:00 - 11:00 AMTitle: An exploration of the moduli spaces of curves. Abstract: This mini-course is meant to be an introduction to various fundamental ideas in moduli spaces theory, through the concrete example of the moduli space of curves. The essential idea is that the geometric structure (i.e. the extra structure one gives to a set of points to turn it into a space, be it a complex manifold, an algebraic variety, scheme etc) of a moduli space is phrased in terms of a functor that describes the moduli problem. This establishes a working dictionary between the geometry of the moduli space and the geometry of families of objects that one wishes to parameterize. We will use this dictionary to understand the basic geometry of the moduli spaces of curves (for example the boundary stratification for the natural compactification to stable curves), to construct natural bundles on the moduli spaces of curves, and to explore the intersection theory of their characteristic classes. | |