Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complex Links and Hilbert-Samuel Multiplicities   We describe a framework for estimating Hilbert-Samuel multiplicities $e_XY$
for pairs of projective varieties $X \subset Y$ from finite point samples
rather than defining equations. The first step involves proving that this
multiplicity remains invariant under certain hyperplane sections which reduce
$X$ to a point $p$ and $Y$ to a curve $C$. Next, we establish that $e_pC$
equals the Euler characteristic (and hence, the cardinality) of the complex
link of $p$ in $C$. Finally, we provide explicit bounds on the number of
uniform point samples needed (in an annular neighborhood of $p$ in $C$) to
determine this Euler characteristic with high confidence.

32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs