# Mathematical Sciences Research Institute

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# Seminar

Commutative Algebra and Algebraic Geometry (Eisenbud Seminar) March 05, 2013 (03:45 PM PST - 06:00 PM PST)
Location: UC Berkeley
Speaker(s) Marti Lahoz
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Commutative Algebra and Algebraic Geometry Seminar
Tuesdays, 3:45-6:00
939 Evans Hall

Organized by David Eisenbud
More information at http://hosted.msri.org/alg/

3:45PM: Symmetric tensors, rank versus cactus rank.
Kristian Ranestad
The cactus rank of a form is the minimal length of an apolar subscheme to the form, and has therefore also been called the scheme length of the form. It is in general smaller than the rank, but its value for a general form is not known. We shall relate it to the dimension of the family of polynomials with given dimension for the space of partials of all orders. I shall report on recent results in work with Bernardi and Marques.

5:00PM: Maximal Cohen-Macaulay modules over cubic hypersurface rings of dimension 4 and 5
Marti Lahoz
In this talk, I will give a new construction of stable Arithmetically Cohen-Macaulay (ACM) bundles on cubic hypersurfaces in $P^{4}$ and $P^{5}$ Our construction relies on the interpretation of MCM modules as objects in the derived category of modules over the even part of the Clifford algebra associated to a quadric fibration. If time permits, I will explain how choices in the threefold case induce different compactifications of the moduli space of Ulrich bundles of rank 2. This is a joint work with Emanuele Macrì and Paolo Stellari.

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