Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Moduli space of factorized ramified connections and generalized
  isomonodromic deformation   We introduce the notion of factorized ramified structure on a generic
ramified irregular singular connection on a smooth projective curve. By using
the deformation theory of connections with factorized ramified structure, we
construct a canonical $2$-form on the moduli space of ramified connections.
Since the factorized ramified structure provides a duality on the tangent space
of the moduli space, the $2$-from becomes nondegenerate. We prove that the
$2$-form on the moduli space of ramified connections is $d$-closed via
constructing an unfolding of the moduli space. Based on the Stokes data, we
introduce the notion of local generalized isomonodromic deformation for generic
unramified irregular singular connections on a unit disk. Applying the
Jimbo-Miwa-Ueno theory to generic unramified connections, the local generalized
isomonodromic deformation is equivalent to the extendability of the family of
connections to an integrable connection. We give the same statement for
ramified connections. Based on this principle of Jimbo-Miwa-Ueno theory, we
construct a global generalized isomonodromic deformation on the moduli space of
generic ramified connections by constructing a horizontal lift of a universal
family of connections. As a consequence of the global generalized isomonodromic
deformation, we can lift the relative symplectic form on the moduli space to a
total closed form, which is called a generalized isomonodromic $2$ form.

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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: hep-ph