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

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    Type
    Article
    Authors
    Lubbes, Niels
    KAUST Department
    Computer Science Program
    Visual Computing Center (VCC)
    Date
    2014-01-01
    Preprint Posting Date
    2013-02-27
    Permanent link to this record
    http://hdl.handle.net/10754/563324
    
    Metadata
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    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.
    Sponsors
    This research was supported by the Austrian Science Fund (FWF): project P21461.
    Publisher
    Walter de Gruyter GmbH
    Journal
    Advances in Geometry
    DOI
    10.1515/advgeom-2014-0007
    arXiv
    arXiv:1302.6684
    Additional Links
    http://arxiv.org/abs/arXiv:1302.6684v2
    ae974a485f413a2113503eed53cd6c53
    10.1515/advgeom-2014-0007
    Scopus Count
    Collections
    Articles; Computer Science Program; Visual Computing Center (VCC)

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