# Rikard Bögvad: How to recognize Hilbert series of graded complete intersections (with generators of different positive degrees)

**Time: **
Mon 2022-11-07 15.00 - 16.00

**Location: **
Zoom

**Video link: **
Meeting ID: 666 5213 9781

**Participating: **
Rikard Bögvad, Stockholm University

### Abstract

Given computational knowledge of just the coefficients \(a_1,a_2,...\) of the Hilbert series of a positively graded Noetherian k-algebra there is an algorithmic criterion that checks (in a non-specified finite number of steps) whether the Hilbert series belongs to a complete intersection. This algorithm was constructed by Thomas Meyer and me in 2004 to analyze some Molien series and I will describe the algorithm. It is the obvious one, but it was tricky (for us) to prove that it works.

There are simple examples that shows that the Hilbert series does not contain information on whether the algebra really is a complete intersection. But in some cases, e.g. if the algebra is known to be Koszul this is possible, as shown in a recent paper by Borzi and D'Ali on cyclotomic Hilbert series, and I will also discuss their results, and some open problems.