Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the behavior of singularities at the $F$-pure threshold   We provide a family of examples where the $F$-pure threshold and the log
canonical threshold of a polynomial are different, but where $p$ does not
divide the denominator of the $F$-pure threshold (compare with an example of
\mustata-Takagi-Watanabe). We then study the $F$-signature function in the case
where either the $F$-pure threshold and log canonical threshold coincide or
where $p$ does not divide the denominator of the $F$-pure threshold. We show
that the $F$-signature function behaves similarly in those two cases. Finally,
we include an appendix which shows that the test ideal can still behave in
surprising ways even when the $F$-pure threshold and log canonical threshold
coincide.

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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph