Deformation of Artinian Algebras and Jordan Type

Proceedings from a specialist session reveal an innovative interplay between deformations of Artinian algebras and Jordan types, examining commuting nilpotent matrices, Specht ideals, and geometric Lefschetz properties. Multiple surveys and studies open new perspectives, uniting questions from Hilbert schemes to local algebra structures.
This volume contains the proceedings of the AMS-EMS-SMF Special Session on Deformations of Artinian Algebras and Jordan Type, held July 18-22, 2022, at the Universite Grenoble Alpes, Grenoble, France.

Articles included are a survey and open problems on deformations and relation to the Hilbert scheme; a survey of commuting nilpotent matrices and their Jordan type; and a survey of Specht ideals and their perfection in the two-rowed case.

Other articles treat topics such as the Jordan type of local Artinian algebras, Waring decompositions of ternary forms, questions about Hessians, a geometric approach to Lefschetz properties, deformations of codimension two local Artin rings using Hilbert-Burch matrices, and parametrization of local Artinian algebras in codimension three. Each of the articles brings new results on the boundary of commutative algebra and algebraic geometry.

Contributor: Anthony Iarrobino (Edited by), Pedro Macias Marques (Edited by), Maria Evelina Rossi (Edited by), Jean Valles (Edited by)

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