Minimal families of curves on surfaces

Handle URI:
http://hdl.handle.net/10754/563809
Title:
Minimal families of curves on surfaces
Authors:
Lubbes, Niels
Abstract:
A 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.
KAUST Department:
Computer Science Program
Publisher:
Elsevier BV
Journal:
Journal of Symbolic Computation
Issue Date:
Nov-2014
DOI:
10.1016/j.jsc.2014.01.003
Type:
Article
ISSN:
07477171
Sponsors:
This research was partly supported by the Austrian Science Fund (FWF): project P21461.
Appears in Collections:
Articles; Computer Science Program

Full metadata record

DC FieldValue Language
dc.contributor.authorLubbes, Nielsen
dc.date.accessioned2015-08-03T12:10:53Zen
dc.date.available2015-08-03T12:10:53Zen
dc.date.issued2014-11en
dc.identifier.issn07477171en
dc.identifier.doi10.1016/j.jsc.2014.01.003en
dc.identifier.urihttp://hdl.handle.net/10754/563809en
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.en
dc.description.sponsorshipThis research was partly supported by the Austrian Science Fund (FWF): project P21461.en
dc.publisherElsevier BVen
dc.subjectAdjunctionen
dc.subjectFamilies of conicsen
dc.subjectMinimal families of curvesen
dc.subjectParametrization degreeen
dc.subjectRoot systemsen
dc.subjectWeak del pezzo surfacesen
dc.titleMinimal families of curves on surfacesen
dc.typeArticleen
dc.contributor.departmentComputer Science Programen
dc.identifier.journalJournal of Symbolic Computationen
kaust.authorLubbes, Nielsen
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