Minimal families of curves on surfaces

Niels Lubbes

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)29-48
Number of pages20
JournalJournal of Symbolic Computation
Volume65
Issue number1
DOIs
StatePublished - Jan 31 2014

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics

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