TY - JOUR

T1 - Minimal families of curves on surfaces

AU - Lubbes, Niels

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This research was partly supported by the Austrian Science Fund (FWF): project P21461.

PY - 2014/1/31

Y1 - 2014/1/31

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/563809

UR - http://arxiv.org/pdf/1302.6687

UR - http://www.scopus.com/inward/record.url?scp=84897023869&partnerID=8YFLogxK

U2 - 10.1016/j.jsc.2014.01.003

DO - 10.1016/j.jsc.2014.01.003

M3 - Article

SN - 0747-7171

VL - 65

SP - 29

EP - 48

JO - Journal of Symbolic Computation

JF - Journal of Symbolic Computation

IS - 1

ER -