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