Time: 9h30, Friday, December 12, 2014

Location:  Room 310, Building A5, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Ha Noi

Abstract:  For a Noetherian local ring (R,m), the Hilbert coefficients of the I-adic filtration of an m-primary ideal I are known to code for properties of R, of the blowup of Spec(R) along V (I), and even of their normalizations. In this note we survey and discuss the main results on the Hilbert coefficients. We give estimations for these coefficients when I is enlarged for general Noetherian local rings. Moreover we introduce some generalizations of the Hilbert coefficients and we relate this new Hilbert coefficients to other numbers introduced in different contexts.