UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

September 03, 2013

939 Evans Hall


3:45PM: Residual Intersections and Duality

David Eisenbud

Let J be an ideal generated by s elements in an s-dimensional regular local ring. If dim S/J = 0, so that J is a complete intersection, then S/J is Gorenstein -- that is, it is self-dual. I will explain an extension of this result to residual intersections -- cases where S/J can have any dimension (and is not even pure dimensional). This is joint work with Bernd Ulrich, inspired by an idea of Duco van Straten.

5:00PM: Higher discriminants and the topology of algebraic maps

Vivek Shende

We introduce `higher discriminants' of a morphism of complex algebraic varieties. These are defined in terms of transversality conditions, and we show: (1) the support of any summand of a projective pushforward of the IC sheaf is a component of a higher discriminant, and (2) any component of the characteristic cycle of a proper pushforward of the constant function is a conormal variety to a component of a higher discriminant.   This talk presents joint work with Luca Migliorini.  

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