Speaker: Nick Addington (Imperial)

Title: Complete Intersections of Quadrics

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, 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 covers becomes singular. I produce a non-Kaehler 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. The example nicely illustrates the modern theory of flops and derived categories.