Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Hilbert function of Artinian local complete intersections of
  codimension three   In singularity theory or algebraic geometry, it is natural to investigate
possible Hilbert functions for special algebras $A$ such as local complete
intersections or more generally Gorenstein algebras. The sequences that occur
as {the} Hilbert functions of standard graded complete intersections are well
understood classically thanks to Macaulay and Stanley. Very little is known in
the local case except in codimension two. In this paper we characterise the
Hilbert functions of quadratic Artinian complete intersections of codimension
three. Interestingly we prove that a Hilbert function is admissible for such a
Gorenstein ring if and only if is admissible for such a complete intersection.
We provide an effective construction of a local complete intersection for a
given Hilbert function. {We prove that the symmetric decomposition of such a
complete intersection ideal is determined by its Hilbert function.}

18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg