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Full Description
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.
Contents
Surveys
Joachim Jelisiejew, Open problems in deformations of Artinian algebras, Hilbert schemes and around
Leila Khatami, Commuting Jordan types: A survey
Chris McDaniel, A brief survey of Specht ideals and their perfection in the two-rowed case
Articles
Nancy Abdallah, A note on Artin Gorenstein algebras with Hilbert function $(1,4,k,k,4,1)$
Nasrin Altafi, A note on Jordan types and Jordan degree types
Elena Angelini, Luca Chiantini and Alessandro Oneto, Waring decompositions of special ternary forms with different Hilbert functions
Vincenzo Antonelli and Gianfranco Casnati, Some remarks on varieties whose twisted normal bundle is an instanton
Edoardo Ballico and Emanuele Ventura, On the Koiran-Skomra's question about Hessians
Davide Bricalli and Filippo Francesco Favale, Standard Artinian algebras and Lefschetz properties: A geometric approach
Luca Chiantini and Fulvio Gesmundo, Decompositions and Terracini loci of cubic forms of low rank
Joan Elias and Maria Evelina Rossi, Almost finitely generated inverse systems and reduced $\mathbf {k}$-algebras
Roser Homs and Anna-Lena Winz, Deformations of local Artin rings via Hilbert-Burch matrices
Shreedevi K. Masuti, The Hilbert function of local Artinian level algebras of codimension $3$ and type $2$
Bernard Mourrain, Isolated singularities, inverse systems and the punctual Hilbert scheme
Liana M. Sega and Deepak Sireeshan, Dg module structures and minimal free resolutions modulo an exact zero divisor
