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COHOMOLOGIA LOCAL CON SOPORTE UN IDEAL MONOMIAL (D-modulos y combinatoria)
 

Summary: COHOMOLOG´IA LOCAL CON SOPORTE UN IDEAL
MONOMIAL (D-m´odulos y combinatoria)
Josep ´Alvarez Montaner
Resum
We study, by using the theory of algebraic D-modules, 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

  

Source: Alvarez Montaner, Josep - Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya

 

Collections: Mathematics