Families of bitangent planes of space curves and minimal non-fibration families

Handle URI:
http://hdl.handle.net/10754/563324
Title:
Families of bitangent planes of space curves and minimal non-fibration families
Authors:
Lubbes, Niels
Abstract:
A cone curve is a reduced sextic space curve which lies on a quadric cone and does not pass through the vertex. We classify families of bitangent planes of cone curves. The methods we apply can be used for any space curve with ADE singularities, though in this paper we concentrate on cone curves. An embedded complex projective surface which is adjoint to a degree one weak Del Pezzo surface contains families of minimal degree rational curves, which cannot be defined by the fibers of a map. Such families are called minimal non-fibration families. Families of bitangent planes of cone curves correspond to minimal non-fibration families. The main motivation of this paper is to classify minimal non-fibration families. We present algorithms which compute all bitangent families of a given cone curve and their geometric genus. We consider cone curves to be equivalent if they have the same singularity configuration. For each equivalence class of cone curves we determine the possible number of bitangent families and the number of rational bitangent families. Finally we compute an example of a minimal non-fibration family on an embedded weak degree one Del Pezzo surface.
KAUST Department:
Computer Science Program
Publisher:
Walter de Gruyter GmbH
Journal:
Advances in Geometry
Issue Date:
1-Jan-2014
DOI:
10.1515/advgeom-2014-0007
ARXIV:
arXiv:1302.6684
Type:
Article
ISSN:
1615715X
Sponsors:
This research was supported by the Austrian Science Fund (FWF): project P21461.
Additional Links:
http://arxiv.org/abs/arXiv:1302.6684v2
Appears in Collections:
Articles; Computer Science Program

Full metadata record

DC FieldValue Language
dc.contributor.authorLubbes, Nielsen
dc.date.accessioned2015-08-03T11:45:45Zen
dc.date.available2015-08-03T11:45:45Zen
dc.date.issued2014-01-01en
dc.identifier.issn1615715Xen
dc.identifier.doi10.1515/advgeom-2014-0007en
dc.identifier.urihttp://hdl.handle.net/10754/563324en
dc.description.abstractA cone curve is a reduced sextic space curve which lies on a quadric cone and does not pass through the vertex. We classify families of bitangent planes of cone curves. The methods we apply can be used for any space curve with ADE singularities, though in this paper we concentrate on cone curves. An embedded complex projective surface which is adjoint to a degree one weak Del Pezzo surface contains families of minimal degree rational curves, which cannot be defined by the fibers of a map. Such families are called minimal non-fibration families. Families of bitangent planes of cone curves correspond to minimal non-fibration families. The main motivation of this paper is to classify minimal non-fibration families. We present algorithms which compute all bitangent families of a given cone curve and their geometric genus. We consider cone curves to be equivalent if they have the same singularity configuration. For each equivalence class of cone curves we determine the possible number of bitangent families and the number of rational bitangent families. Finally we compute an example of a minimal non-fibration family on an embedded weak degree one Del Pezzo surface.en
dc.description.sponsorshipThis research was supported by the Austrian Science Fund (FWF): project P21461.en
dc.publisherWalter de Gruyter GmbHen
dc.relation.urlhttp://arxiv.org/abs/arXiv:1302.6684v2en
dc.subjectassociated curvesen
dc.subjectcurve correspondencesen
dc.subjectdevelopable surfaceen
dc.subjectminimal non-fibration familiesen
dc.subjectSpace curvesen
dc.subjectweak Del Pezzo surfaceen
dc.titleFamilies of bitangent planes of space curves and minimal non-fibration familiesen
dc.typeArticleen
dc.contributor.departmentComputer Science Programen
dc.identifier.journalAdvances in Geometryen
dc.identifier.arxividarXiv:1302.6684en
kaust.authorLubbes, Nielsen
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