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Workshop

The infinite Euclidean Distance discriminant

  • Emil Horobet (Sapientia Hungarian University of Transylvania, Romania)
Felix-Klein-Hörsaal Universität Leipzig (Leipzig)

Abstract

In this talk, we study the infinite ED discriminant, the variety of data points with infinite critical points of the distance function from themselves to a given variety. We present many examples of varieties that have such a discriminant, and we show that this relates to instances of morphisms where we do not have the purity of the branch locus, we give sufficient conditions on the varieties to have a non-empty infinite discriminant and finally, we classify all such curves in arbitrary dimension and all surfaces in three-space which have a one-dimensional infinite discriminant, via the explicit construction of all such surfaces.

conference
29.07.24 02.08.24

MEGA 2024

MPI für Mathematik in den Naturwissenschaften Leipzig (Leipzig) E1 05 (Leibniz-Saal)
Universität Leipzig (Leipzig) Felix-Klein-Hörsaal

Mirke Olschewski

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Saskia Gutzschebauch

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Christian Lehn

Ruhr-Universität Bochum

Irem Portakal

Max Planck Institute for Mathematics in the Sciences

Rainer Sinn

Universität Leipzig

Bernd Sturmfels

Max Planck Institute for Mathematics in the Sciences

Simon Telen

Max Planck Institute for Mathematics in the Sciences

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