Complete Intersections of Quadrics
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Tue, 08/02/2011 14:00 |
Nicolas Addington (Imperial College London) |
Algebraic and Symplectic Geometry Seminar  |
SR1 |
| There is a long-studied correspondence between intersections of two quadrics and hyperelliptic curves, first noticed by Weil and since used as a testbed for many fashionable theories: Hodge theory, motives, and moduli of vector bundles in the '70s and '80s, derived categories in the '90s, non-commutative geometry and mirror symmetry today. The story generalizes to three, four, and more quadrics, exhibiting new geometric behaviour at each step. The case of four quadrics nicely illustrates the modern theory of flops and derivced categories and, as a special case, gives a pair of derived-equivalent Calabi-Yau 3-folds. | |||