\documentclass[11pt]{article}


\begin{document}
\begin{center}
Maria Evelina Rossi

\bigskip
{\sc The Castelnuovo-Mumford regularity of the tangent cone of a local 
ring}

\bigskip

{\bf Abstract}

\end{center}
\noindent 
We will discuss some results contained in a recent joint work with 
N.V.Trung and G.Valla. We proved that the Castelnuovo-Mumford regularity 
of the tangent cone of a local ring $A$ is effectively bounded by the 
dimension and any cohomological degree of $A.$
From this it follows that there are only a finite number of Hilbert-Samuel 
functions of local rings with given dimension and  cohomological degree. 
Upper bounds are given for the Hilbert coefficients in terms of such 
invariants.
In particular our approach gives an easier proof of recent results of 
Srinivas and Trivedi on the finiteness of Hilbert functions.





\end{document}
-- 
------------------ooOOO---------------OOOoo---------------------------------


Maria Evelina Rossi                      tel:     +39 010 3536948
Universita' di Genova                  fax:    +39 010 3536752
Dipartimento di Matematica         Home: +39 010 6045009
Via Dodecaneso 35                        E-mail: rossim@dima.unige.it
16146-Genova                 
------------------ooOOO---------------OOOoo---------------------------------