Normal factorization in SL(2, Z) and the confluence of singular fibers in elliptic fibrations
| dc.citation.journalTitle | Beitrage Zur Algebra Und Geometrie | |
| dc.contributor.author | Cadavid, C.A. | |
| dc.contributor.author | Vélez, J.D. | |
| dc.contributor.department | Universidad EAFIT. Departamento de Ciencias | spa |
| dc.contributor.researchgroup | Matemáticas y Aplicaciones | spa |
| dc.creator | Cadavid, C.A. | |
| dc.creator | Vélez, J.D. | |
| dc.date.accessioned | 2021-04-12T14:04:18Z | |
| dc.date.available | 2021-04-12T14:04:18Z | |
| dc.date.issued | 2009-01-01 | |
| dc.description.abstract | In this article we obtain a result about the uniqueness of factorization in terms of conjugates of the matrix of, of some matrices representing the conjugacy classes of those elements of SL(2,Z) arising as the monodromy around a singular fiber in an elliptic fibration (i.e. those matrices that appear in Kodaira's list). Namely we prove that if M is a matrix in Kodaira's list, and M = G1 ···Gr where each Gi is a conjugate of U in SL(2,Z), then after applying a finite sequence of Hurwitz moves the product G1 ···Gr can be transformed into another product of the form H1 ···HnG'n+1 ···G'r where H1 ···Hn is some fixed shortest factorization of M in terms of conjugates of U, and G'n+1 ···G'r = Id2×2. We use this result to obtain necessary and sufficient conditions under which a relatively minimal elliptic fibration without multiple fibers f: S ? D = {z ? C: |z| < 1}, admits a weak deformation into another such fibration having only one singular fiber. © 2009 Heldermann Verlag. | eng |
| dc.identifier | https://eafit.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=1891 | |
| dc.identifier.issn | 01384821 | |
| dc.identifier.issn | 21910383 | |
| dc.identifier.other | SCOPUS;2-s2.0-70450195119 | |
| dc.identifier.uri | http://hdl.handle.net/10784/27690 | |
| dc.language.iso | eng | eng |
| dc.publisher | Springer Verlag | |
| dc.relation.uri | https://www.scopus.com/inward/record.uri?eid=2-s2.0-70450195119&partnerID=40&md5=f798034a27551dde8b03e2fda278bb0d | |
| dc.rights | https://v2.sherpa.ac.uk/id/publication/issn/0138-4821 | |
| dc.source | Beitrage Zur Algebra Und Geometrie | |
| dc.title | Normal factorization in SL(2, Z) and the confluence of singular fibers in elliptic fibrations | eng |
| dc.type | article | eng |
| dc.type | info:eu-repo/semantics/article | eng |
| dc.type | info:eu-repo/semantics/publishedVersion | eng |
| dc.type | publishedVersion | eng |
| dc.type.local | Artículo | spa |