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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


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.

Belongs to: Department of Mathematics
Last changed: Jan 14, 2020