Nasrin Altafi Razlighi: Hilbert function of points in projective space

This seminar will be helt via Zoom, the meeting ID is 646 8203 3933

Abstract

The n-dimensional real projective space is defined to be the set of all lines through the origin in \(\mathbb{R}^{n+1}\). Similar definition works for any field. We explain why algebraic geometers work over projective spaces. Any finite set of points in a projective space imposes independent linear conditions on homogeneous polynomials which determines the Hilbert function. The Hilbert function is an important invariant in algebraic geometry for computing the dimension and the degree of an algebraic variety, i.e., zero locus of polynomial equations.

We then discuss the relation between configuration of a set of points and its Hilbert function.