UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

March 03, 2015

939 Evans Hall

3:45PM: Tor as a module over an exterior algebra

David Eisenbud

The "CI operators" defined on free resolutions over a complete intersection R give a module structure on Ext_R(M,k) that is the main tool for analyzing such resolutions. Burke and Schreyer and I have discovered a series of higher operators extending this idea. I will explain the classical theory and an interesting context in which these higher operators appear.

5:00PM: Nondegenerate Plane Curves: Classically and Tropically

Ralph Morrison

The moduli space of curves of genus g is a much-studied object in algebraic geometry, and has a tropical analog parametrizing metric graphs of genus g. In 2009, Castryck and Voight studied the locus (inside the classical moduli space) of curves that could be represented in a nondegenerate way by a Laurent polynomial. I will introduce the tropical analog of this space, called the moduli space of tropical plane curves. After showing that this space has the expected dimension from classical algebraic geometry, I will show how to explicitly compute this space for low genus, and will illustrate nontrivial obstructions to realizing tropical curves in the plane. This is based on joint work with Sarah Brodsky, Michael Joswig, and Bernd Sturmfels.

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