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

Tid: Må 2020-01-20 kl 15.30 - 16.30

Föreläsare: Nasrin Altafi, KTH

### 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.

Innehållsansvarig:webmaster@math.kth.se
Tillhör: Institutionen för matematik