Seminar Event Detail

Student Commutative Algebra

Date:  Tuesday, November 28, 2017
Location:  4088 East Hall (3:00 PM to 4:00 PM)

Title:  Eagon-Northcott complexes

Abstract:   Given a map of free modules, one can define the Eagon-Northcott complex, which often provides a resolution of the ideal of maximal minors of the map. This generalizes the Koszul complex, and has similar exactness and duality properties. Moreover, these complexes provide a unified framework for many of our favorite examples in algebraic geometry, including rational normal curves and scrolls and the vanishing loci of minors of 1-generic matrices. In this talk, we'll define these complexes, sketch their basic properties, and give some basic examples and applications. We'll then give an application of Gruson, Lazarsfeld, and Peskine of the Eagon-Northcott complex to the Castelnuovo-Mumford regularity of curves in projective space. Time permitting, we'll also sketch Kempf's construction of Eagon-Northcott-type complexes as pushforwards of a Koszul complex on a Grassmannian bundle. The talk will be elementary and no knowledge beyond basic commutative algebra will be required.


Speaker:  Devlin Mallory
Institution:  University of Michigan

Event Organizer:   Robert Walker


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