Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On invariant of the regularity index of fat points   We prove invariant of the regularity index of fat points under changes of the
linear subspace containing the support of the fat points. Then we show that
Segre's bound is attained by any set of s non-degenerate equimultiple fat
points in $\mathbb P^n$, $s\le n+3$. We also give an example showing that there
always exists a set of n+4 non-degenerate equimultiple fat points in $\mathbb
P^n$ such that Segre's bound is not attained.

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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
3
The categories of this paper are: physics
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio