Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Small elementary components of Hilbert schemes of points   We answer an open problem posed by Iarrobino in the '80s: is there an
elementary component of the Hilbert scheme of points
$\textrm{Hilb}^d(\mathbb{A}^n)$ with dimension less than $(n-1)(d-1)$? We
construct an infinite class of such components in
$\textrm{Hilb}^d(\mathbb{A}^4)$. Our techniques also allow us to construct an
explicit example of a local Artinian ring with trivial negative tangents,
vanishing nonnegative obstruction space, and socle-dimension $2$.

15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex