# Nasrin Altafi: Jordan types for graded Artinian algebras in height two

**Time: **
Mon 2020-01-20 15.30 - 16.30

**Lecturer: **
Nasrin Altafi, KTH

**Location: **
Kräftriket, house 5, room 35

### Abstract

Multiplication by a linear form \(\ell\) on an Artinian algebra \(A\) determines a nilpotent linear operator on \(A\), the Jordan type of this operator, \(P_{\ell,A}\), is an integer partition of the dimension of \(A\) as a vector space. The weak Lefschetz and the strong Lefschetz properties of \(A\) can be determined from the Jordan type of a generic \(\ell\) of \(A\).

The cell associated to a partition \(P\) of \(n\) is defined as the cell of all graded Artinian quotients \(A=k[x,y]/I\) such that the initial ideal of \(I\) is a monomial ideal \(E_P\) determined by \(P\). For a given partition \(P\), we determine the minimal number of generators of a generic ideal \(I\subset k[x,y]\) in the associated cell such that \(P\) is the Jordan type of \(A\) for some linear form \(\ell\in A\).

This is joint work with A. Iarrobino, L. Khatami and J. Yaméogo.