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Nicolas Addington (Imperial)
Wednesday 03 November 2010, 14:15-15:15
Complete intersections of quadrics
- đ¤ Speaker: Nicolas Addington (Imperial)
- đ Date & Time: Wednesday 03 November 2010, 14:15 - 15:15
- đ Venue: MR13, CMS
Abstract
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.
Series This talk is part of the Algebraic Geometry Seminar series.
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