Abstract
AbstractThis is the content of four lectures on Rees rings and their defining equations delivered at the CIME workshop Recent developments in Commutative Algebra held at Levico Terme (Trento), Italy on July 1–5, 2019. The Rees ring and the special fiber ring of an ideal arise in the process of blowing up a variety along a subvariety. Rees rings and special fiber rings also describe, respectively, the graphs and the images of rational maps between projective spaces. A difficult open problem in commutative algebra, algebraic geometry, elimination theory, and geometric modeling is to determine explicitly the equations defining graphs and images of rational maps. In these lectures we will discuss this topic in several situations.
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