\title[Local Cohomology Modules of Stanley-Reisner Rings]
{Local Cohomology of Stanley-Reisner Rings \\
with supports in General Monomial Ideals}
\author{Victor Reiner}
\address{School of Mathematics\\
University of Minnesota\\
Minneapolis, MN 55455, USA}
\author{Volkmar Welker}
\address{Fachbereich Mathematik und Informatik\\
Philipps-Universit\"at Marburg\\
35032 Marburg, Germany}
\author{Kohji Yanagawa}
\address{Department of Mathematics,
Graduate School of Science, Osaka University, Toyonaka, Osaka  560, Japan}
\maketitle

ABSTRACT: We study the local cohomology modules of a Stanley-Reisner ring 
associated to a simplicial complex with support in the ideal corresponding 
to a subcomplex. We give a combinatorial topological formula for the 
multigraded Hilbert series, and in the case where the ambient complex is 
Gorenstein, compare this with a second combinatorial formula that generalizes 
results of Mustata and Terai. The agreement between these two formulae is 
seen to be a disguised form of Alexander duality. Other results include a 
comparison of the local cohomology with certain Ext modules, results about 
when it it is concentrated in a single homological degree, and combinatorial 
topological interpretations of some vanishing theorems.