UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

March 14, 2017

939 Evans Hall

3:45PM: A new approach to contact problems in geometry

Joe Harris

Geometric problems involving order of contact---for example, how many flexes does a plane curve of degree $d$ have?---can often be solving by considering the relevant {\it bundle of principle parts}. When we're dealing with a family of varieties, though---for example, in a pencil of plane curves of degree $d$, how many have hyperflexes?---difficulties arise: some members of the family will have singularities, and at those singularities the bundle of relative principle parts will no longer be locally free. We will describe two approaches to dealing with this problem: one proposed and carried out by Ziv Ran, and a new one found by Anand Patel and Ashvin Swaminathan.

5:00PM: The implicitization problem for rational normal scrolls

Alessio Sammartano

We study the defining ideals of the Rees algebra and of the special fiber ring for ideals of a rational normal scroll in P^n. In particular, we show that these rings are Koszul algebras.

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