UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

January 26, 2016

939 Evans Hall

3:45PM: Duality for Residual Intersections

David Eisenbud

A variety (or scheme) X of codimension s in Projective space is a complete intersection if it’s ideal is generated by s forms; it is called an s-residual intersection of a scheme Y if the union of X and Y is defined by s forms. Residual intersections play an important role in algebraic geometry and commutative algebra. Some typical examples beyond complete intersections are the (sufficiently general) varieties defined by the maximal minors of a matrix of forms. I’ll describe several contexts in which this notion arises, including the “liaison” classification of curves in P3 and some classical problems of intersection theory, and sketch some new results from a joint paper with Bernd Ulrich, in which we provide duality results for residual intersections extending some of the familar ideas of duality for complete intersections.

5:00PM: Chapter 1 of “3264 & All That”

Student seminar

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