Families of bitangent planes of space curves and minimal non-fibration families
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Niels Lubbes
Abstract
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.
© 2014 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- On the type number of a hypersurface in the 6-dimensional sphere
- On the equality case in Ehrhart’s volume conjecture
- Hamiltonian stability of Hamiltonian minimal Lagrangian submanifolds in pseudo- and para-Kähler manifolds
- The holomorphic symplectic structures on hyper-Kähler manifolds of type A∞
- Bifurcation values and stability of algebras of bounded polynomials
- Families of bitangent planes of space curves and minimal non-fibration families
- On deformations of G2-structures by Killing vector fields
- Cohomology of 3-points configuration spaces of complex projective spaces
- Slope stability of Fano fourfolds with respect to smooth surfaces
- On quartics with lines of the second kind
Articles in the same Issue
- Frontmatter
- On the type number of a hypersurface in the 6-dimensional sphere
- On the equality case in Ehrhart’s volume conjecture
- Hamiltonian stability of Hamiltonian minimal Lagrangian submanifolds in pseudo- and para-Kähler manifolds
- The holomorphic symplectic structures on hyper-Kähler manifolds of type A∞
- Bifurcation values and stability of algebras of bounded polynomials
- Families of bitangent planes of space curves and minimal non-fibration families
- On deformations of G2-structures by Killing vector fields
- Cohomology of 3-points configuration spaces of complex projective spaces
- Slope stability of Fano fourfolds with respect to smooth surfaces
- On quartics with lines of the second kind
