Self-intersections of surfaces that contain two circles through each point

2024/09/28 by Lubbes, Niels
#14C20 #14J17 #14P25 #51B10 #51M15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2409.19253

Abstract

We classify the singular loci of real surfaces in three-space that contain two circles through each point. We characterize how a circle in such a surface meets this loci as it moves in its pencil and as such provide insight into the topology of the surface.

Related

• Shapes of surfaces that contain a great and a small circle through each point
• Self-intersections are empirically Gaussian
• The Topology of Surface Singularities
• A surface with q=2 and canonical map of degree 16
• Intersections of curves on surfaces and their applications to mapping class groups