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Commutative Algebra Seminar

Resolutions of ideals associated to subspace arrangements
Thursday, October 11, 2018
3:00-4:00 PM
4088 East Hall Map
Suppose that W_1,W_2, ... ,W_d are subspaces of an n-dimensional K-vector space and let J_1, J_2, ... , J_d in K[x_1, x_2, ... , x_n] be the vanishing ideals of W_1, W_2, ...,W_d . Conca and Herzog showed that the Castelnuovo-Mumford regularity of the product of these ideals is equal to d. Derksen and Sidman showed that the Castelnuovo-Mumford regularity of the intersection of these ideals is at most d. In my work I show that analogous results hold when we replace the polynomial ring with the exterior algebra and work over a field of characteristic 0. The proofs of aforementioned theorems rely on the existence of non-zero divisors, so this approach fails for the exterior algebra. Instead, we rely on the functoriality of free resolutions and construct a functor F from the category of polynomial functors to itself. The functor F transforms resolutions of ideals in the polynomial ring into resolutions of ideals in the exterior algebra. Speaker(s): Francesca Gandini (University of Michigan)
Building: East Hall
Event Type: Workshop / Seminar
Tags: Mathematics
Source: Happening @ Michigan from Department of Mathematics