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Generating sequences and Poincaré series for a finite set of plane divisorial valuations
dc.contributor.author | Galindo, Carlos | |
dc.contributor.author | Delgado, Félix | |
dc.contributor.author | Núñez, A. | |
dc.date.accessioned | 2010-06-09T10:19:53Z | |
dc.date.available | 2010-06-09T10:19:53Z | |
dc.date.issued | 2008 | |
dc.identifier.issn | 00018708 | |
dc.identifier.uri | http://hdl.handle.net/10234/13553 | |
dc.description.abstract | Let V be a finite set of divisorial valuations centered at a 2- dimensional regular local ring R. In this paper we study its structure by means of the semigroup of values, SV , and the multi-index graded algebra defined by V , grV R. We prove that SV is finitely generated and we compute its minimal set of generators following the study of reduced curve singularities. Moreover, we prove a unique decomposition theorem for the elements of the semigroup. The comparison between valuations in V , the approximation of a reduced plane curve singularity C by families of sets V (k) of divisorial valuations, and the relationship between the value semigroup of C and the semigroups of the sets V (k), allow us to obtain the (finite) minimal generating sequences for C as well as for V . We also analyze the structure of the homogeneous components of grV R. The study of their dimensions allows us to relate the Poincaré series for V and for a general curve C of V . Since the last series coincides with the Alexander polynomial of the singularity, we can deduce a formula of A’Campo type for the Poincar´e series of V . Moreover, the Poincar´e series of C could be seen as the limit of the series of V (k), k ≥ 0 | |
dc.format.extent | 23 p. | |
dc.language.iso | eng | |
dc.publisher | Elsevier | |
dc.relation.isPartOfSeries | Advances in mathematics; vol. 219, núm. 5 | |
dc.rights.uri | http://rightsstatements.org/vocab/CNE/1.0/ | * |
dc.subject.other | Matemàtica | |
dc.title | Generating sequences and Poincaré series for a finite set of plane divisorial valuations | |
dc.type | info:eu-repo/semantics/article | |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
dc.type.version | info:eu-repo/semantics/sumittedVersion |
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