Show simple item record

dc.contributor.authorLubbes, Niels
dc.date.accessioned2015-08-03T12:10:53Z
dc.date.available2015-08-03T12:10:53Z
dc.date.issued2014-01-31
dc.identifier.citationLubbes, N. (2014). Minimal families of curves on surfaces. Journal of Symbolic Computation, 65, 29–48. doi:10.1016/j.jsc.2014.01.003
dc.identifier.issn07477171
dc.identifier.doi10.1016/j.jsc.2014.01.003
dc.identifier.urihttp://hdl.handle.net/10754/563809
dc.description.abstractA minimal family of curves on an embedded surface is defined as a 1-dimensional family of rational curves of minimal degree, which cover the surface. We classify such minimal families using constructive methods. This allows us to compute the minimal families of a given surface.The classification of minimal families of curves can be reduced to the classification of minimal families which cover weak Del Pezzo surfaces. We classify the minimal families of weak Del Pezzo surfaces and present a table with the number of minimal families of each weak Del Pezzo surface up to Weyl equivalence.As an application of this classification we generalize some results of Schicho. We classify algebraic surfaces that carry a family of conics. We determine the minimal lexicographic degree for the parametrization of a surface that carries at least 2 minimal families. © 2014 Elsevier B.V.
dc.description.sponsorshipThis research was partly supported by the Austrian Science Fund (FWF): project P21461.
dc.publisherElsevier BV
dc.relation.urlhttp://arxiv.org/pdf/1302.6687
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in [JournalTitle]. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in [JournalTitle], [[Volume], [Issue], (2014-01-31)] DOI: 10.1016/j.jsc.2014.01.003 . © 2014. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rightsThis file is an open access version redistributed from: http://arxiv.org/pdf/1302.6687
dc.subjectAdjunction
dc.subjectFamilies of conics
dc.subjectMinimal families of curves
dc.subjectParametrization degree
dc.subjectRoot systems
dc.subjectWeak del pezzo surfaces
dc.titleMinimal families of curves on surfaces
dc.typeArticle
dc.contributor.departmentComputer Science Program
dc.contributor.departmentVisual Computing Center (VCC)
dc.identifier.journalJournal of Symbolic Computation
dc.rights.embargodate2016-01-31
dc.eprint.versionPost-print
dc.identifier.arxivid1302.6687
kaust.personLubbes, Niels


This item appears in the following Collection(s)

Show simple item record