 
Summary: COHOMOLOG´IA LOCAL CON SOPORTE UN IDEAL
MONOMIAL (Dm´odulos y combinatoria)
Josep ´Alvarez Montaner
Resum
We study, by using the theory of algebraic Dmodules, the local cohomology modules
supported on a monomial ideal I of the polynomial ring R = k[x1, . . . , xn], where k
is a field of characteristic zero. We compute the characteristic cycle of Hr
I (R) and
Hp
P(Hr
I (R)), where P is an homogeneous prime ideal of R. By using these results we
can describe the support of these modules, in particular we can decide when the local
cohomology module Hr
I (R) vanishes in terms of the minimal primary decomposition of
the monomial ideal I, compute the Bass numbers of Hr
I (R) and describe its associated
primes. The characteristic cycles also give some invariants of the ring R/I. We use
these invariants to compute the Hilbert function of R/I, the minimal free resolutions
of squarefree monomial ideals and the cohomology groups of the complement of an
arrangement of linear varieties given by the monomial ideal I. Finally, we determine
