University of Sydney

    School of Mathematics and Statistics

    Algebraic Geometry Seminar

    11:00-12:30 in Carslaw 709 on Wednesday 2 May.

    Gavin Brown

    K3 surfaces and graded rings

    K3 surfaces are one of the four classical families of (minimal) surfaces occupying the "kappa = 0" part of the classification (the analogous place for surfaces where elliptic curves fit in the curve classification).

    I'll start by giving three or four ways of thinking about K3 surfaces together with the usual first examples. But the main point is that polarised K3 surfaces with small `numerical data' have graded coordinate rings that are Gorenstein in smallish codimension, smallish here being about 4. These are on the boundary of explicit methods for working with Gorenstein rings --- there are famous classification theorems in codimensions 1,2,3.

    Two things will happen. First I will show lots of examples of K3 surfaces and Gorenstein rings, some fairly exotic. Second I will show how the method of `unprojection' relates these Gorenstein rings and can be strong enough in practice to replace a classification theorem.
     
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