Type
ArticleAuthors
Lubbes, NielsKAUST Department
Computer Science ProgramVisual Computing Center (VCC)
Date
2014-01-31Embargo End Date
2016-01-31Permanent link to this record
http://hdl.handle.net/10754/563809
Metadata
Show full item recordAbstract
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.2014.01.003Sponsors
This research was partly supported by the Austrian Science Fund (FWF): project P21461.Publisher
Elsevier BVJournal
Journal of Symbolic ComputationarXiv
1302.6687Additional Links
http://arxiv.org/pdf/1302.6687ae974a485f413a2113503eed53cd6c53
10.1016/j.jsc.2014.01.003