Chennai Mathematical Institute


On the behaviour of the Castelnuovo-Mumford regularity
Dr. Clare D'Cruz
Chennai Mathematical Institute.
21-11-03 (Institute Colloquium)


In this paper we are concerned with examples which will shed some light on certain questions concerning this behaviour. One simple question which was open is: Does the regularity increase if we pass to the radical or remove embedded primes? By examples, we show that this happens. As a by-product we are also able to answer some related questions.

In particular, we provide examples of licci ideals related to monomial curves in ${\bf P}^{3}$ (resp. in ${\bf P}^{4}$) such that the regularity of their radical is essentially the square (resp. the cube) of that of the ideal.