Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lagrangian constant cycle subvarieties in Lagrangian fibrations   We show that the image of a dominant meromorphic map from an irreducible
compact Calabi-Yau manifold $X$ whose general fiber is of dimension strictly
between $0$ and $\dim X$ is rationally connected. Using this result, we
construct for any hyper-K\"ahler manifold $X$ admitting a Lagrangian fibration
a Lagrangian constant cycle subvariety $\Sigma_H$ in $X$ which depends on a
divisor class $H$ whose restriction to some smooth Lagrangian fiber is ample.
If $\dim X = 4$, we also show that up to a scalar multiple, the class of a
zero-cycle supported on $\Sigma_H$ in $\mathrm{CH}_0(X)$ depend neither on $H$
nor on the Lagrangian fibration (provided $b_2(X) \ge 8$).

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The categories of this paper are: solv-int
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The categories of this paper are: stat
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
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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: gr-qc
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The categories of this paper are: cmp-lg