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Workshop

Symmetric Ideals, Invariant Hilbert Schemes and Stabilization

  • Andreas Kretschmer
E1 05 (Leibniz-Saal)

Abstract

Symmetric ideals are ideals in a polynomial ring which are stable under all permutations of the variables. They appear at prominent places in algebraic combinatorics and asymptotic commutative algebra. A global study of zero-dimensional symmetric ideals is the study of the invariant Hilbert scheme for the action of the n-th symmetric group on affine n-space. In this talk I will introduce invariant Hilbert schemes in this setting and explain our irreducibility and smoothness results for certain cases. We have also classified all homogeneous symmetric ideals giving rise to a representation of dimension at most 2n and we can decide which of them define singular points of the invariant Hilbert scheme. I will end with several open questions. This is joint work with Sebastian Debus.

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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