Mathematics Research Institute


Hilbert Function and µ-generic Artin Algebras

Hema Srinivasan (University of Missouri)

Fecha: 13/06/2017 12:30
Lugar: Seminario A125. Facultad de Ciencias

Suppose $R$ is a polynomial ring in $n$ variables and $I$ is a homogeneous ideal of height $n$ in $R$ so that $R/I$ is an Artin Algebra. Let $\mu(I)$ denote the minimum number of generators for $I$. If the Hilbert function of $R/I$ is of the form $(1, n, { n\choose 2 }+1, \ldots , n, 1)$ then there are $n$ quadratic generators of $I$. Suppose these generators generate an ideal $I_2$ of height 1. Then we show that there is an upper bound for the number of generators of $I$ in terms of $n$ and a Gorenstein ideal $J$ with embedding dimension $n-1$. We say an ideal $I$ is $\mu$ generic if $\mu(I)$ has this upper bound. We give some criterion when this is achieved and some consequences for the Unmorality of Hilbert functions for a class of co-dimension three Artin algebras.