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Finding Rational Curves through Prescribed Points

Modern Mathematics: An Introduction to MSRI's 2008-09 Programs October 10, 2007 - October 11, 2007

October 10, 2007 (04:30PM PDT - 05:30PM PDT)
Speaker(s): Brendan Hassett (Rice University)
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Abstract 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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