On the branch curve of a general projection of a surface to a plane
Ciro Ciliberto, Flaminio Flamini
TL;DR
This paper proves that the branch curve resulting from a general projection of a surface onto a plane is irreducible and only has nodes and cusps, clarifying its geometric properties.
Contribution
It establishes the irreducibility and singularity types of the branch curve for general surface projections, a result not previously confirmed.
Findings
Branch curve is irreducible
Branch curve has only nodes and cusps
Provides geometric characterization of the branch curve
Abstract
In this paper we prove that the branch curve of a general projection of a surface to the plane is irreducible, with only nodes and cusps.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Algebraic Geometry and Number Theory