Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nodal curves and Riccati solutions of Painlev\'e equations   In this paper, we study Riccati solutions of Painlev\'e equations from a view
point of geometry of Okamoto-Painlev\'e pairs $(S,Y)$. After establishing the
correspondence between (rational) nodal curves on $S-Y$ and Riccati solutions,
we give the complete classification of the configurations of nodal curves on
$S-Y$ for each Okamoto-Painlev\'e pair $(S, Y)$. As an application of the
classification, we prove the non-existence of Riccati solutions of Painlev\'e
equations of types $P_{I}, P_{III}^{\tilde{D}_8}$ and $P_{III}^{\tilde{D}_7}$.
We will also give a partial answer to the conjecture in (STT) and (T) that the
dimension of the local cohomology $H^1_{Y_{red}}(S,\Theta_S(-\log Y_{red}))$ is
one.

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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: econ