Triple lines on a cubic threefold
Gloire Grace Bockondas, Samuel Boissiere
TL;DR
This paper investigates the geometric properties of lines on smooth complex cubic threefolds, focusing on the singularities of a specific curve on the Fano surface associated with lines of the second type.
Contribution
It provides a detailed description of the singularities of the curve of lines of the second type on the Fano surface of a cubic threefold.
Findings
Characterization of singularities of the curve of lines of the second type
Insights into the structure of the Fano surface for cubic threefolds
Enhanced understanding of line configurations on cubic threefolds
Abstract
The present paper deals with lines contained in a smooth complex cubic threefold. It is well-known that the set of lines of the second type on a cubic threefold is a curve on its Fano surface. Here we give a description of the singularities of this curve.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Geometry and complex manifolds