TY - JOUR

T1 - Families of bitangent planes of space curves and minimal non-fibration families

AU - Lubbes, Niels

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

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/563324

UR - http://arxiv.org/abs/arXiv:1302.6684v2

UR - http://www.scopus.com/inward/record.url?scp=84908114101&partnerID=8YFLogxK

U2 - 10.1515/advgeom-2014-0007

DO - 10.1515/advgeom-2014-0007

M3 - Article

VL - 14

SP - 647

EP - 682

JO - Advances in Geometry

JF - Advances in Geometry

SN - 1615-7168

IS - 4

ER -