Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Motives and the Hodge Conjecture for moduli spaces of pairs   Let $C$ be a smooth projective curve of genus $g\geq 2$ over $\mathbb C$. Fix
$n\geq 1$, $d\in {\mathbb Z}$. A pair $(E,\phi)$ over $C$ consists of an
algebraic vector bundle $E$ of rank $n$ and degree $d$ over $C$ and a section
$\phi \in H^0(E)$. There is a concept of stability for pairs which depends on a
real parameter $\tau$. Let ${\mathfrak M}_\tau(n,d)$ be the moduli space of
$\tau$-polystable pairs of rank $n$ and degree $d$ over $C$. Here we prove that
for a generic curve $C$, the moduli space ${\mathfrak M}_\tau(n,d)$ satisfies
the Hodge Conjecture for $n \leq 4$. For obtaining this, we prove first that
${\mathfrak M}_\tau(n,d)$ is motivated by $C$.

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The categories of this paper are: chem-ph
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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: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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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: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph