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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

Plats: 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.

Innehållsansvarig:webmaster@math.kth.se
Tillhör: Institutionen för matematik
Senast ändrad: 2020-01-14