3.30 pm, Seminar Hall
General hyperplane restriction theorems
Purdue University, U.S.A.
In the study of Hilbert functions, one of the most useful tools is Green's hyperplane section theorem, which involves studying how Hilbert functions change under general hyperplane restrictions. This enables one to give a sharp upper bound for the Hilbert function of R/hR, where R is a standard graded K-algebra and h is a general linear form, in terms of the Hilbert function of R. This result of Green has been extended to the case of general homogeneous polynomials by Herzog and Popescu, and by Gasharov. I will present further generalization of these theorems obtained in a joint work with Satoshi Murai.