Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geography of Genus 2 Lefschetz fibrations   Questions of geography of various classes of $4$-manifolds have been a
central motivating question in $4$-manifold topology. Baykur and Korkmaz asked
which small, simply connected, minimal $4$-manifolds admit a genus $2$
Lefschetz fibration. They were able to classify all the possible homeomorphism
types and realize all but one with the exception of a genus $2$ Lefschetz
fibration on a symplectic $4$-manifold homeomorphic, but not diffeomorphic to
$3 \mathbb{CP}^2 \# 11\overline{\mathbb{CP}}^2$. We give a positive
factorization of type $(10,10)$ that corresponds to such a genus $2$ Lefschetz
fibration. Furthermore, we observe two restrictions on the geography of genus
$2$ Lefschetz fibrations, we find that they satisfy the Noether inequality and
a BMY like inequality. We then find positive factorizations that describe genus
$2$ Lefschetz fibrations on simply connected, minimal symplectic $4$-manifolds
for many of these points.

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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex