| Abstract |
Many interesting classes of algebraic varieties can be studied in terms of their corresponding graded rings. In many interesting cases the corresponding ring is a Gorenstein ring. One can construct algebraic varieties in codimension less than and equal to 3 by using the structure theorems of the corresponding Gorenstein rings. In codimension greater than 3, one method of constructing algebraic varieties is the technique of unprojection. The aim of this talk is to explain the idea of unprojection by explicit examples. In particular, I will focus on two matrix formats, Tom and Jerry which gives the construction of algebraic varieties in codimension 4 via unprojection of 3 dimensional algebraic varieties.
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