UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

February 19, 2008

939 Evans Hall

3:45PM: The Shape of Minimal Free Resolutions II

David Eisenbud

I'll explain ideas from the proof of the Boij-Soederberg conjectures, and the connection with the cohomology of vector bundles that it exploits. This is recent work with Frank Schreyer.

5:00PM: Some results on inhomogeneous discriminants

Angelica Cueto

We study generalized Horn-Kapranov rational parametrizations of inhomogeneous sparse discriminants from both a theoretical and an algorithmic perspective. In particular, we focus on the computation of inhomogeneous discriminants related to integer matrices $B$ as an implicitization problem with base points corresponding to a H-K parametrization $\psi_B$. We show that all these parametrizations are birational refining a previous result by Kapranov and prove some results on the corresponding implicit equations. We also propose a combinatorial algorithm to compute the degree of inhomogeneous discriminantal surfaces associated to uniform matrices. If time permits, we will present some examples that show numerous difficulties for computing the (Hilbert-Samuel) multiplicities of these points. Joint work with Alicia Dickenstein.

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