A sign that used to annoy me, and still does
AT Ricolfi - Journal of Geometry and Physics, 2024 - Elsevier
We provide a proof of the following fact: if a complex scheme Y has Behrend function
constantly equal to a sign σ∈{±1}, then all of its components Z⊂ Y are generically reduced …
constantly equal to a sign σ∈{±1}, then all of its components Z⊂ Y are generically reduced …
Open problems in deformations of Artinian algebras, Hilbert schemes and around
J Jelisiejew - arXiv preprint arXiv:2307.08777, 2023 - arxiv.org
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 …
such as algebras, modules or tensors. We list both the well-known ones and some new ones …
A counterexample to the parity conjecture
F Giovenzana, L Giovenzana, M Graffeo… - arXiv preprint arXiv …, 2023 - arxiv.org
Let $[Z]\in\text {Hilb}^ d\mathbb A^ 3$ be a zero-dimensional subscheme of the affine three-
dimensional complex space of length $ d> 0$. Okounkov and Pandharipande have …
dimensional complex space of length $ d> 0$. Okounkov and Pandharipande have …
Irrational components of the Hilbert scheme of points
We construct irrational irreducible components of the Hilbert scheme of points of affine n-
dimensional space, for n at least 12. We start with irrational components of the Hilbert …
dimensional space, for n at least 12. We start with irrational components of the Hilbert …
Unexpected but recurrent phenomena for Quot and Hilbert schemes of points
F Giovenzana, L Giovenzana, M Graffeo… - arXiv preprint arXiv …, 2024 - arxiv.org
We investigate some aspects of the geometry of two classical generalisations of the Hilbert
schemes of points. Precisely, we show that parity conjecture for $\text {Quot} _r^ d\mathbb …
schemes of points. Precisely, we show that parity conjecture for $\text {Quot} _r^ d\mathbb …
The Hilbert scheme of points on a threefold, I
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 …
broken Gorenstein structure for finite schemes, and show that its existence guarantees …
Generically nonreduced components of Hilbert schemes on fourfolds
J Jelisiejew - arXiv preprint arXiv:2406.19782, 2024 - arxiv.org
We exhibit generically nonreduced components of the Hilbert scheme of at least $21 $
points on a smooth variety of dimension at least four. The result was announced in …
points on a smooth variety of dimension at least four. The result was announced in …
Conjectural criteria for the most singular points of the Hilbert schemes of points
F Rezaee - Experimental Mathematics, 2024 - Taylor & Francis
We provide conjectural necessary and (separately) sufficient conditions for the Hilbert
scheme of points of a given length to have the maximum dimension tangent space at a point …
scheme of points of a given length to have the maximum dimension tangent space at a point …