UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

February 01, 2011

939 Evans Hall

3:45PM: Stable Ulrich Bundles

Robin Hartshorne

An Ulrich bundle is a vector bundle on a projective variety $X$ that has no intermediate cohomology (called ACM bundle) and has the maximum number $dr$ of generators of the associated graded module, where $d = $degree of $X$ and $r =$ rank of bundle. We show the existence of stable Ulrich bundles of all ranks $r \geq 2$ on a nonsingular cubic surface in $P^3$, and of all even ranks $= 2$ on a nonsingular cubic threefold in $P^4$. (joint work with Marta Casanellas)}

5:00PM: Matroids and the inverse of a linear space

Cynthia Vinzant

Given a linear space L, we will find a universal Groebner basis and Hilbert series of the prime ideal I of polynomials vanishing on the coordinate-wise reciprocal of L. To do this, we'll degenerate this ideal into the Stanley-Reisner ideal of a broken circuit complex, which is a simplicial complex associated to the matroid of L. This talk will be following a paper of Proudfoot and Speyer (arXix:0410069).

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