Journal article
Combinatorics of multigraded Poincaré series for monomial rings
Journal of algebra, v 308(1), 73
01 Feb 2007
Abstract
Backelin proved that the multigraded Poincaré series for resolving a residue field over a polynomial ring modulo a monomial ideal is a rational function. The numerator is simple, but until the recent work of Berglund there was no combinatorial formula for the denominator. Berglund's formula gives the denominator in terms of ranks of reduced homology groups of lower intervals in a certain lattice. We now express this lattice as the intersection lattice
L
A
(
I
)
of a subspace arrangement
A
(
I
)
, use Crapo's Closure Lemma to drastically simplify the denominator in some cases (such as monomial ideals generated in degree two), and relate Golodness to the Cohen–Macaulay property for associated posets. In addition, we introduce a new class of finite lattices called
complete lattices, prove that all geometric lattices are complete and provide a simple criterion for Golodness of monomial ideals whose lcm-lattices are complete.
Metrics
Details
- Title
- Combinatorics of multigraded Poincaré series for monomial rings
- Creators
- Alexander Berglund - Stockholm UniversityJonah Blasiak - University of California, BerkeleyPatricia Hersh - Indiana University Bloomington
- Publication Details
- Journal of algebra, v 308(1), 73
- Publisher
- Elsevier
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000244267400006
- Scopus ID
- 2-s2.0-33751432865
- Other Identifier
- 991021862255404721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics