Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gauss-Manin Lie algebra of mirror elliptic K3 surfaces   We study mirror symmetry of families of elliptic K3 surfaces with elliptic
fibers of type $E_6,~E_7$ and $E_8$. We consider a moduli space $\mathsf{T}$ of
the mirror K3 surfaces enhanced with the choice of differential forms. We show
that coordinates on $\mathsf{T}$ are given by the ring of quasi modular forms
in two variables, with modular groups adapted to the fiber type. We furthermore
introduce an algebraic group $\mathsf{G}$ which acts on $\mathsf{T}$ from the
right and construct its Lie algebra $\mathrm{Lie}(\mathsf{G})$. We prove that
the extended Lie algebra generated by $\mathrm{Lie}(\mathsf{G})$ together with
modular vector fields on $\mathsf{T}$ is isomorphic to
$\mathrm{sl}_2(\mathbb{C})\oplus\mathrm{sl}_2(\mathbb{C})$.

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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph