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Finding Rational Curves through Prescribed Points
October 10, 2007 (04:30 PM PDT - 05:30 PM PDT)
Brendan Hassett (Rice University)
It is a postulate of Euclidean geometry that through any two points in the plane there passes a unique line. A theorem of high-school geometry asserts the existence of a circle through any three non-collinear points. Lines and circles are instances of rational curves, and one central problem of modern algebraic geometry is to understand the rational curves passing through a given configuration of points in a surface (or higher-dimensional space). We review recent results and open problems that will be addressed at the MSRI program in Spring 2009.
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