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.
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
Anthony Iarrobino, Northeastern University, Boston, MA, Pedro Macias Marques, University of Evora, Portugal, Maria Evelina Rossi, University of Genoa, Italy, and Jean Valles, Universite de Pau et des Pays de l'Adour, France.
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