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 Ir, where I = I1, I2, . . . ,Ir, are Cohen-Macaulay ideals of equal height and for all i = j, Ii + Ij 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.