Algebra Seminar

Date & Time: Friday, January 16, 2009, 11:30-12:30.
Venue: Ramanujan Hall

Title: On the Chern Number of an Ideal

Speaker: Mousumi Mandal, IIT Bombay

Abstract: It is shown that for a parameter ideal J of a finitely generated module M over a local ring, the chern number e₁(J,M)&le 0. Vasconcelos' Negativity Conjecture has been settled for certain unmixed quotients of regular local rings by explicitly finding the Hilbert polynomial of any parameter ideal in a local ring S/I where (S,n) is a regular local ring and I = I₁ &cap I₂ &cap . . . &cap I_r, where I = I₁, I₂, . . . ,I_r, are Cohen-Macaulay ideals of equal height and for all i = j, I_i + I_j are n-primary. Goto's solution to Vasconcelos' negativity conjecture has been presented. i.e., if R is a Noetherian local ring of positive dimension and Q is a parameter ideal, then R is Cohen-Macaulay if and only if R is unmixed and e₁(Q)=0.