UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

December 13, 2011

939 Evans Hall

3:45PM: Limit linear series: an updated survey

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. After reviewing their original theory, we will discuss how an alternative point of view sheds new light both on the original construction, and on various generalizations.

5:00PM: Hilbert functions of fat points in $P^2$

David Berlekamp

What Hilbert functions can arise for symbolic powers of ideals of points in projective space? How is the Hilbert function or Betti table of such a scheme constrained by the Hilbert function of its support? I will describe some of what is known for some special configurations and small numbers of points in $P^2$, and how the problem becomes qualitatively and vastly more complicated as the number of points in question increases from, say, 5 to 12.

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