Afshin Goodarzi: A question regarding the associated primes of the generic initial ideals
Tid: Må 2018-11-05 kl 11.00 - 12.00
Plats: Room 31, building 5, Kräftriket, Department of Mathematics, Stockholm University
Medverkande: Afshin Goodarzi
Abstract:
Let R be a polynomial ring over a field of characteristic zero. Let gin(J) denote the generic initial ideal of a graded ideal J in R with respect to the reverse lexicographic order. The Crystallization Principle asserts that if J is generated in degrees less than k, and gin(J) has no generator in degree k, then gin(J) is generated in degrees less than k. The Crystallization Principle is also valid over the exterior algebra, where the theory of Alexander duality provides a "dual version" of this principle. Does this dual version hold also in the symmetric algebra?
I will provide the necessary background and more motivations to look at this problem.
Let R be a polynomial ring over a field of characteristic zero. Let gin(J) denote the generic initial ideal of a graded ideal J in R with respect to the reverse lexicographic order. The Crystallization Principle asserts that if J is generated in degrees less than k, and gin(J) has no generator in degree k, then gin(J) is generated in degrees less than k. The Crystallization Principle is also valid over the exterior algebra, where the theory of Alexander duality provides a "dual version" of this principle. Does this dual version hold also in the symmetric algebra?
I will provide the necessary background and more motivations to look at this problem.