Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: On the tangent space to the Hilbert scheme of points in $P^3$

Seminar | April 16 | 5-6 p.m. | 939 Evans Hall

 Ritvik Ramkumar, UC Berkeley

 Department of Mathematics

The Hilbert scheme of n points in $P^2$ is smooth of dimension 2n and the tangent space to any (monomial) ideal admits a nice combinatorial description. On the other hand the Hilbert scheme of n points in $P^3$ is singular and there is a conjecture on what the monomial ideal with the largest tangent space dimension should be. By extending the combinatorial methods used in $P^2$, we give a proof of a major portion of the conjecture (in a sense we will describe). Along the way we will strengthen previous bounds on the dimension of the tangent space. This is joint (ongoing) work with Alessio Sammartano.