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    Minimal families of curves on surfaces

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    Type
    Article
    Authors
    Lubbes, Niels
    KAUST Department
    Computer Science Program
    Visual Computing Center (VCC)
    Date
    2014-01-31
    Embargo End Date
    2016-01-31
    Permanent link to this record
    http://hdl.handle.net/10754/563809
    
    Metadata
    Show full item record
    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.
    Citation
    Lubbes, N. (2014). Minimal families of curves on surfaces. Journal of Symbolic Computation, 65, 29–48. doi:10.1016/j.jsc.2014.01.003
    Sponsors
    This research was partly supported by the Austrian Science Fund (FWF): project P21461.
    Publisher
    Elsevier BV
    Journal
    Journal of Symbolic Computation
    DOI
    10.1016/j.jsc.2014.01.003
    arXiv
    1302.6687
    Additional Links
    http://arxiv.org/pdf/1302.6687
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.jsc.2014.01.003
    Scopus Count
    Collections
    Articles; Computer Science Program; Visual Computing Center (VCC)

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