Speaker: Professor C. Polini (University of Notre Dame)

Thời gian: 10:00 đến 11:00 Ngày 10/07/2025

Địa điểm: C102, VIASM

TITLE: Singularities of a rational curve and the Rees algebra of the forms that parametrize the curve ABSTRACT: I will discuss how to read the singularities of a rational curve in projective space through the syzygy matrix of the forms parametrizing them. A rational curve C of degree d can be parametrized by forms of degree d in the polynomial ring k[x,y], and the syzygy matrix F of these forms is easier to handle and often reveals more information than the implicit equation of C. Our goals are to read information about the singularities of C solely from the matrix F, to set up a correspondence between the types of singularities on the one hand and the shapes of the syzygy matrices on the other hand, and to use this correspondence to stratify the space of rational plane curves of a given degree. We will also explore the correspondence between the types of singularities of C and the defining ideal of the blowup algebra of the ideal I generated by the forms parametrizing the forms.