Time: 9h00, Wednesday, April 20, 2016
Location: Room 4, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi
Abstract: Linear resolutions are typically considered to be the most simple among minimal free resolutions of graded modules. The linearity defect of a module measures how far a it is from having a linear free resolution. Over a polynomial ring, ideals with linearity defect zero are exactly componentwise linear ideals. I will focus on clarifying the significance of the linearity defect in a combinatorial setting, specifically, that of edge ideals. A motivation comes from Fröberg's theorem on edge ideals with linear resolutions, which can be seen as a classification of edge ideals with linearity defect zero. The theory of Betti splittings and Sega's characterization of the linearity defect play an important role in our study.
Joint work with Vu Quang Thanh