Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
Local cohomology, free resolutions, and Tor modules
When S is a standard Z-graded polynomial extension of a ring R, the Castelnuovo-Mumford regularity of a graded S-module can be defined in four ways: in terms of vanishing degrees for local cohomology supported in the variables, vanishing degrees for Tor modules, shifts appearing in graded free S-resolutions, and degrees for which the truncation of the module has a linear free resolution. We will present some extensions of the equivalence of these definitions to the more general situation that corresponds to a product of projective spaces over R, in place of a projective space over R. Illustrating examples will concern Rees algebras and points in a product of two projective spaces over a field.
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