39 citations · 121 across the 34 of their papers we have counts for
38 papers
Hankel and Multiplication Tensor Completions for Cactus Rank
Alessandra Bernardi, Joachim Jelisiejew, Oriol Reig Fité
We show that the Hankel flat extension formulation of the cactus algorithm is equivalent to a completion problem for multiplication tensors of Artinian Gorenstein algebras. The unk…
Unrestrictions and concise secant varieties
Jakub Jagiełła, Joachim Jelisiejew
We introduce the concise secant varieties, which are, informally speaking, modular partial desingularisations of secant varieties to Segre embeddings. More precisely, they are proj…
On a conjecture by Michael Wemyss regarding the calculation of GV invariants
Joachim Jelisiejew, Agata Smoktunowicz
Contraction algebras are noncommutative algebras introduced by Donovan and Wemyss to classify of 3-dimensional flops. Wemyss conjectures that contraction algebras can be deformed t…
Detecting Direct Sums of Tensors and Their Limits
S. Canino, C. Flavi, J. Jelisiejew
We generalize Mammana's classification of limits of direct sums to more than two factors. We also extend it from polynomials to arbitrary Segre-Veronese format, generalising and un…
The Iarrobino scheme: a self-dual analogue of the Hilbert scheme of points
Joachim Jelisiejew
For a fixed quasi-projective scheme we introduce a self-dual analogue of which we call the Iarrobino scheme of . It is a fine moduli space of zero-dim…
The Hilbert scheme of points on a threefold: broken Gorenstein structures and linkage
Joachim Jelisiejew, Ritvik Ramkumar, Alessio Sammartano
We investigate the Hilbert scheme of points on a smooth threefold. We introduce a notion of broken Gorenstein structure for finite schemes, and show that its existence guarantees s…
Classification and degenerations of small minimal border rank tensors via modules
Jakub Jagiełła, Joachim Jelisiejew
We give a self-contained classification of -generic minimal border rank tensors in for . Together with previ…
Symmetric powers: structure, smoothability, and applications
Cosimo Flavi, Joachim Jelisiejew, Mateusz Michałek
We investigate border ranks of twisted powers of polynomials and smoothability of symmetric powers of algebras. We prove that the latter are smoothable. For the former, we obtain u…
Generically nonreduced components of Hilbert schemes on fourfolds
Joachim Jelisiejew
We exhibit generically nonreduced components of the Hilbert scheme of at least points on a smooth variety of dimension at least four. The result was announced in~[Jelisiejew__…
Open problems in deformations of Artinian algebras, Hilbert schemes and around
Joachim Jelisiejew
We review the open problems in the theory of deformations of zero-dimensional objects, such as algebras, modules or tensors. We list both the well-known ones and some new ones that…
The variety of polar simplices II
Joachim Jelisiejew, Kristian Ranestad, Frank-Olaf Schreyer
We discuss the space of ideals with Hilbert function that are apolar to a full rank quadric . We prove that its components of saturated ideals are…
Limits of saturated ideals
Joachim Jelisiejew, Tomasz Mańdziuk
We investigate the question whether a given homogeneous ideal is a limit of saturated ones. We provide cohomological necessary criteria for this to hold and apply them to a range o…
Hilbert schemes of points and applications
Joachim Jelisiejew
The thesis concerns Hilbert schemes of points and apart from mathematical results, contains small open problems and history sections, see the introduction for more details. The the…
Concise tensors of minimal border rank
Joachim Jelisiejew, J. M. Landsberg, Arpan Pal
We determine defining equations for the set of concise tensors of minimal border rank in when and the set of concise minimal border rank -gen…
On the Hilbert function of Artinian local complete intersections of codimension three
Joachim Jelisiejew, Shreedevi K. Masuti, M. E. Rossi
In singularity theory or algebraic geometry, it is natural to investigate possible Hilbert functions for special algebras such as local complete intersections or more generally…
On construction of k-regular maps to Grassmannians via algebras of socle dimension two
Joachim Jelisiejew, Hanieh Keneshlou
A continuous map is -regular if the -dimensional subspaces corresponding to images of any distinct points span a -dimensional space. For $τ…
Components and singularities of Quot schemes and varieties of commuting matrices
Joachim Jelisiejew, Klemen Šivic
We investigate the variety of commuting matrices. We classify its components for any number of matrices of size at most 7. We prove that starting from quadruples of size 8 matrices…
Hermitian K-theory via oriented Gorenstein algebras
Marc Hoyois, Joachim Jelisiejew, Denis Nardin +1
We show that the hermitian K-theory space of a commutative ring R can be identified, up to A^1-homotopy, with the group completion of the groupoid of oriented finite Gorenstein R-a…
Bounds on complexity of matrix multiplication away from CW tensors
Roser Homs, Joachim Jelisiejew, Mateusz Michałek +1
We present three families of minimal border rank tensors: they come from highest weight vectors, smoothable algebras, or monomial algebras. We analyse them using Strassen's laser m…
Białynicki-Birula decomposition for reductive groups in positive characteristic
Joachim Jelisiejew, Łukasz Sienkiewicz
We prove the existence of Bialynicki-Birula decomposition for Kempf monoids, which is a large class that contains for example monoids with reductive unit group in all characteristi…
The Hilbert scheme of infinite affine space and algebraic K-theory
Marc Hoyois, Joachim Jelisiejew, Denis Nardin +2
We study the Hilbert scheme from an -homotopical viewpoint and obtain applications to algebraic K-theory. We show that the Hilber…
Pathologies on the Hilbert scheme of points
Joachim Jelisiejew
We prove that the Hilbert scheme of points on a higher dimensional affine space is non-reduced and has components lying entirely in characteristic p for all primes p. In fact, we s…
Smoothable zero dimensional schemes and special projections of algebraic varieties
Joachim Jelisiejew, Grzegorz Kapustka, Michal Kapustka
We study the degrees of generators of the ideal of a projected Veronese variety to depending on the center of projection. Thi…
Białynicki-Birula decomposition for reductive groups
Joachim Jelisiejew, Łukasz Sienkiewicz
We generalize the Białynicki-Birula decomposition from actions of on smooth varieties to actions of linearly reductive group on finite type schemes and algebraic sp…