Title: Generic plane curves, infinitely near points and local quadratic transforms.
Speaker: William Heinzer - Purdue University
Abstract: The term generic in the title relates to properties of the extension ring R(t) of a commutative ring R. Infinitely near points is a term used by Zariski and more recently Lipman to describe the regular local rings of dimension at least two obtained as local quadratic transforms of a regular local ring. If I=(a,b)R is an ideal primary for the maximal ideal of a two- dimensional regular local ring R, then P=(bt-a)R(t) is a principal prime ideal of R(t) and D=R(t)/P is a one- dimensional Noetherian local domain. Properties of D such as its multiplicity reflect properties of the origin as a singular point of the generic curve defined by bt=a.
