Rational curves in Calabi-Yau threefolds: towards classification and contractibility

Franco Rota (University of Glasgow)

Tuesday 14th January 15:00-16:00 Maths 311B

Abstract

I'll talk about my work in progress here in Glasgow, with Michael Wemyss and Gavin Brown.
Deciding whether a subvariety of an algebraic variety is contractible is a deep problem of algebraic geometry. Even when the subvariety is a single smooth rational curve C, the question is extremely subtle.

We assume moreover that the ambient variety is a Calabi-Yau threefold.
When C is contractible, its contraction algebra (which pro-represents the deformation theory of C) governs much of the geometry. Our expectation is that deformation theory not only controls contractibility but detects it, even when C is not known to contract.

I will introduce the key ideas and tools of this game, and describe the (partial) results we have gotten so far.

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