UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

October 14, 2008

939 Evans Hall

3:45PM: From stable curves to higher dimensions

Valery Alexeev

Location: 740 Evans

Applications of stable curves and maps to enumerative geometry, physics, arithmetical geometry, symplectic geometry, etc., are very well known. Due to efforts by many people, this theory was partially extended to higher dimensions, when stable curves are replaced by stable surfaces, 3-folds, etc. I will attempt to describe the current state of the art in this field.

5:00PM: Linear series on curves and graphs

Matt Baker

Location: 740 Evans

I will discuss some unexpectedly rich analogies between algebraic curves and finite graphs, including graph theoretic-analogues of the Jacobian, the Riemann-Roch theorem, and hyperellipticity. I will then discuss how specialization of linear series from the generic fiber of a regular semistable arithmetic surface to the dual graph of the special fiber provides a concrete link between these two worlds.

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