Seminar
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| Location: | SLMath: Online/Virtual, Eisenbud Auditorium |
Infinite free resolutions- an inside view
Abstract: Specifying a finitely generated standard graded ring R over a finite field, or over the rational numbers, and specifying a finitely generated R-module M, together involve only a finite amount of data; but the minimal R-free resolution F of M is typically infinite, and except in special cases, no finite description of F is known.
Most of the work on infinite resolutions in the last 50 years has focused on the sequence of ranks of the free modules in F -- an "outside" view. But with tools such as Macaulay2, it is increasingly easy to examine some of the maps and syzygy modules in F directly, an "inside" view.
I will explain some of the history of these problems, and describe recent observations and results from my work with Hai Long Dao, Bernd Ulrich and Claudia Polini.
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