Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Small Lefschetz Fibrations on Simply-Connected $4$-Manifolds   We consider simply-connected $4$-manifolds admitting Lefschetz fibrations
over the $2$-sphere. We explicitly construct nonhyperelliptic and hyperelliptic
Lefschetz fibrations of genus $4$ on simply-connected $4$-manifolds which are
exotic symplectic $4$-manifolds in the homeomorphism classes of
$\mathbb{C}P^{2}\#8\overline{\mathbb{C} P^{2}}$ and $\mathbb{C}
P^{2}\#9\overline{\mathbb{C} P^{2}}$, respectively. From these, we provide
upper bounds for the minimal number of singular fibers of such fibrations. In
addition, we prove that this number is equal to $18$ for $g=3$ when such
fibrations are hyperelliptic. Moreover, we discuss these numbers for higher
genera.

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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc