Algebraic Geometry Seminar
Bernd Ulrich
Purdue
Distance in free resolutions and iterated socles: constructions and applications
Abstract: Iterated socles of modules over a local ring are
obtained by repeated formations of socles. Iterated
socles are ubiquitous, and one of the goals of the
talk is to give explicit formulas for the generators
of iterated socles in terms of the matrices in a free
resolution of the original module. In addition, we
obtain bounds on iterated socles using the new notion
of distance in free resolutions, which serves as a
substitute for degree shifts in resolutions that are
not necessarily graded. This circle of ideas has
applications to integral closures of ideals, depths of
associated graded rings, and resolutions of multiplier
ideals.
Wednesday April 22, 2015 at 4:00 PM in SEO 427