Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deformation Theory of Log Pseudo-holomorphic Curves and Logarithmic
  Ruan-Tian Perturbations   In a previous paper [FT1], for any logarithmic symplectic pair (X,D) of a
symplectic manifold X and a simple normal crossings symplectic divisor D, we
introduced the notion of log pseudo-holomorphic curve and proved a compactness
theorem for the moduli spaces of stable log curves. In this paper, we introduce
a natural set up for studying the deformation theory of log (and relative)
curves. As a result, we obtain a logarithmic analog of the space of Ruan-Tian
perturbations for these moduli spaces. For a generic compatible pair of an
almost complex structure and a log perturbation term, we prove that the
subspace of simple maps in each stratum is cut transversely. Such perturbations
enable a geometric construction of Gromov-Witten type invariants for certain
semi-positive pairs (X, D) in arbitrary genera. In future works, we will use
local perturbations and a gluing theorem to construct log Gromov- Witten
invariants of arbitrary such pair (X, D).

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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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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: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph