UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

December 10, 2013

939 Evans Hall

3:45PM: Minimal regularity schemes with fixed Hilbert polynomial

David Berlekamp

I'll present results from the paper http://arxiv.org/abs/1307.2707, providing a construction of closed, projective, characteristic 0 schemes which have minimal Castelnuovo-Mumford regularity among those with a specified Hilbert polynomial, as well as those which have minimal regularity given a specified Hilbert function. Among other things, this completes the provision of examples bounding the range of possibilities for the regularity given fixed Hillbert polynomial, and interestingly, both extremes are attained by monomial ideals.

5:00PM: Vanishing of Tor and why we care about it

Justin Chen

Following the paper http://arxiv.org/abs/1302.2170 of the same title, I will give a survey of various results dealing with the structure and vanishing of Tor modules, many of which are in the following spirit: if M, N are R-modules, assuming property P holds for M \otimes N, what can be said about Tor^R_i(M, N) and in turn, M and N? Examples will be provided.

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