| Abstract: A standard geometric procedure to study the singularities of an algebraic variety is to examine their blowups. Algebraically, this corresponds to understanding the structure of the Rees algebra R(I) of the ideal I defining the singularity. Although in general this is a difficult task, sometimes R(I) can be described as a quotient of a polynomial ring modulo an ideal generated by polynomials that are either linear or define the special fiber of the blowup. Ideals of the latter kind are said to be of fiber type. In this talk, I will discuss classes of ideals for which the fiber-type property is connected with their combinatorial structure, including ideals of star configurations and symmetric strongly shifted ideals. The content of this talk is part of joint work with B. Drabkin, L. Guerrieri, and A. Seceleanu. |