Alladi Ramakrishnan Hall

Monomial ideals with tiny squares

Shalom Eliahou

ULCO

Let I be an ideal in the 2-variable polynomial ring K[x,y], minimally
generated by m monomials. How many generators are needed to generate the square of
I? It was widely expected that I^2 would require at least 2m-1 generators. Is this
true? In this talk, we will provide a rather surprising complete answer to this
question, achieved this past summer in a joint work with Jürgen Herzog and Maryam
Mohammadi Saem. The requirements to follow the talk are, well… minimal.