MSI Colloquium

4pm Thursday 31 July 2003 (MSI Colloquium)

Miles Reid
University of Warwick

Introduction to classification of varieties

The classification of complex algebraic varieties can be motivated by ideas from school algebra, from Euclidean and non-Euclidean geometry, or from the first pictures in a topology course. "Small" corresponds to easy equations of low degree, problems having solutions in terms of rational or elementary functions, geometries of positive curvature, simply connected surfaces, and so on; "medium sized" corresponds to the first nontrivial cases, elliptic functions and elliptic curves ("quadratic in y equals cubic in x") flat geometries, infinite Abelian fundamental group, integrable systems; "big" geometries correspond to all the remaining "hard" cases, Riemann surfaces of genus > 2, negative curvature, positive canonical class. The talk follows to some extent the introductory section of my ICM2002 talk although some idea of the contents can be found in the Appendix to Chapter 2 of my baby textbook [UAG] Miles Reid, Undergraduate algebraic geometry, CUP.




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