UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

March 04, 2008

939 Evans Hall

3:45PM: Ulrich bundles on cubic surfaces

Robin Hartshorne

Let X be a nonsingular cubic surface in P^3. We prove the existence, for every rank r at least 2, of stable Ulrich bundles of rank r on X. An Ulrich bundle is a vector bundle with no intermediate cohomology, whose associated graded module has the largest possible number, 3r, of generators. These bundles form an open subset of dimension r^2 + 1 of the moduli space of stable vector bundles on X. This is joint work with Marta Casanellas.

5:00PM: The structure of the tautological rings

Jameel Al-Aidroos

The structure of the tautological rings The tautological rings of the moduli spaces of pointed curves contain valuable geometric data about the moduli spaces and the curves parameterized by those spaces. And study of the tautological rings is also motivated by their combinatorial nature and their (conjectured) remarkable algebraic structure. It's possible to appreciate the structure of the rings with very little knowledge of the moduli spaces themselves, and the talk aims at that goal. I'll show you how a typical calculation in the tautological rings is translated into a question of graph combinatorics. I'll talk about the overarching conjecture that guides much of the study of these rings, and about two strategies for tackling that conjecture.

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