Complete intersections of quadrics

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• Nicolas Addington (Imperial)
• Wednesday 03 November 2010, 14:15-15:15
• MR13, CMS.

If you have a question about this talk, please contact Burt Totaro.

There is a long-studied correspondence between intersections of two quadrics and hyperelliptic curves. It was first noticed by Weil in the 50s and has since been a testbed for many theories: Hodge theory and motives in the 70s, derived categories in the 90s, Floer theory and mirror symmetry today. The two spaces are connected by some moduli problems with a very classical flavor, involving lots of lines on quadrics, or more fashionably by matrix factorizations.

The story extends easily to intersections of three quadrics and double covers of P^2, but going to four quadrics, the double cover becomes singular. I produce a non-Kahler resolution of singularities with a clear geometric meaning, and relate its derived category to that of the intersection. As a special case I get a pair of derived-equivalent Calabi-Yau 3-folds, which are of interest in mirror symmetry.

This talk is part of the Algebraic Geometry Seminar series.

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