Algebra and Combinatorics Seminar

Date: January 25, 2019

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Aleksandra Sobieska, TAMU

Title: Minimal Free Resolutions over Rational Normal Scrolls

Abstract: Free resolutions of monomial ideals over the polynomial ring are well-studied and reasonably well-understood, though they are still an active area of research in commutative algebra. However, resolutions over quotients of the polynomial ring are much more mysterious, and even simple examples can violate the nicer properties that the polynomial ring provides. Starting in the 1990's, there is some work on resolutions over toric rings, a particular (and well-behaved) quotient of the polynomial ring. In this talk, we will present a minimal free resolution of the ground field over a specific toric ring that arises from rational normal scrolls. We also provide a computation of the Betti numbers for the resolution of the ground field for all rational normal $k$-scrolls.