UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

September 02, 2014

939 Evans Hall

3:45PM: Recent progress on limit linear series

Brian Osserman

Linear series are fundamental to the study of algebraic curves, and the most powerful technique to date for studying linear series is the theory of limit linear series, a degeneration technique introduced by Eisenbud and Harris. However, for the past nearly 30 years, several foundational questions relating to limit linear series have remained open, including how to generalize them from curves of compact type to more general nodal curves. I will describe how the discovery of an equivalent definition of limit linear series has opened the door to solutions of many of these questions.

5:00PM: Deformations of Complex Poisson manifolds and their Lagrangian Submanifolds

Ziv Ran

We study compact Kaehlerian manifolds endowed with a holomorphic Poisson structure, i.e. a tangent 2-vector with zero self-bracket, which is almost everywhere nondegenerate. Under a normal-crossing condition on the degeneracy divisor, we prove these manifolds have unobstructed deformations, along with their 'Lagrangian', i.e. maximal isotropic, submanifolds. The proof is based on Deligne's mixed Hodge theory.

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