Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Lefschetz standard conjecture for Lagrangian covered
  hyper-K\"ahler varieties   We investigate the Lefschetz standard conjecture for degree $2$ cohomology of
hyper-K\"ahler manifolds admitting a covering by Lagrangian subvarieties. In
the case of a Lagrangian fibration, we show that the Lefschetz standard
conjecture is implied by the SYZ conjecture characterizing classes of divisors
associated with Lagrangian fibration. In dimension $4$, we consider the more
general case of a Lagrangian covered fourfold $X$, and prove the Lefschetz
standard conjecture in degree $2$, assuming $\rho(X)=1$ and $X$ is general in
moduli. Finally we discuss various links between Lefschetz cycles and the study
of the rational equivalence of points and Bloch-Beilinson type filtrations,
giving a general interpretation of a recent intriguing result of Marian and
Zhao.

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The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
1
The categories of this paper are: cs
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The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
3
The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ