UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

March 06, 2018

939 Evans Hall

3:45PM: A new residual intersection phenomenon

David Eisenbud

Residual intersection theory works well for ideals like the ideal of pxp minors of a generic p x (p+1) matrix, but fails for some very nice ideals, such as the ideal of 2 x 2 minors of a 2 x n matrix for n greater than 3. Poking around for what might be true, Bernd Ulrich and I stumbled on a new phenomenon that seems to be rather general. We are far from proving all that seems to be true, but I'll describe our conjectures and results, which at least cover the 2 x n matrices. This is joint work of mine with Bernd Ulrich and Craig Huneke.

5:00PM: Applications of the Excess intersection formula

Irit Huq-Kuruvilla

In this talk, we introduce the excess intersection formula and use it to compute the number of cubics tangent to 5 given ones. If there is more time, we will discuss intersections of surfaces in a curve and discrete points.

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