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Next Meeting

University of Bristol - Thursday 15th November

The next meeting of the COW will take place at the University of Bristol on Thursday 15th November. The meeting will start at 2pm. All talks will be held in the 4th floor seminar room of Howard House (please note that this is not the School of Mathematics).

Schedule

Time Speaker Title
2:00pm Nick Shepherd-Barron Local Aspects of the Schottky Problem for Algebraic Surfaces
3:30pm Jan Stevens The Moduli Space of Twisted Cubics
5:00pm Marina Logares Integrable Systems and Higgs Bundles

Abstracts

Nick Shepherd-Barron (King's College London) - Local Aspects of the Schottky Problem for Algebraic Surfaces
An explicit plumbing construction introduced by Fay leads to an explicit local description of the image of moduli spaces under the period map. For curves the results go back to Poincare; we show that something comparable happens for surfaces.
Jan Stevens (Gothenburg) - The Moduli Space of Twisted Cubics
We present a smooth and functorial compactification of the space of twisted cubics. A twisted cubic is a smooth rational curve of degree three in projective 3-space. It is unique up to a change of coordinates, so there exists a 12 dimensional family of such curves in 3-space. A natural compactification is provided by the Hilbert scheme of space curves with Hilbert polynomial 3t+1. This Hilbert scheme has two smooth components, the smallest one of which contains the twisted cubics as an open subset. We describe a compactification with good geometric properties, that represents a functor. It is given by the space of Cohen-Macaulay curves, as introduced by Hønsen, parametrising Cohen-Macaulay curves together with a finite morphism to projective space which is assumed to be an isomorphism outside a finite number of points.
Marina Logares (Plymouth) - Integrable Systems and Higgs Bundles
The moduli space of Higgs bundles is a rich geometric object which lies in the interface of algebraic geometry, differential geometry and mathematical physics. One of its properties is that it carries the structure of an algebraic completely integrable system known as the Hitchin system. We will talk about the Hitchin system and discuss a variation of it providing a complex partially integrable system. This talk is based on joint work with I. Biswas and A. Peón-Nieto.

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