2.00 pm - 3:15 pm, Seminar Hall
Minkowski's inequalities for multiplicities of ideals
Let (R,m) be a d-dimensional noetherian local ring and I and J m-primary ideals. For integers i between 0 and d, there are positive integers e_i(I|J) called the mixed multiplicites of (I,J). In 1973, B. Teissier conjectured two inequalities about mixed multiplicities, proving them for reduced Cohen-Macaulay algebras over algebraically closed fields of characteristic zero. D. Rees and R. Y. Sharp in 1978 proved Teissier's conjectures for all Noetherian local rings. We shall explain their solution. We shall also discuss the case when equalities hold in these conjectures and show that it leads to a generalisation of the Rees multiplicity theorem.