Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complex $\text{G}_2$ and Associative Grassmannian   We obtain defining equations of the smooth equivariant compactification of
the Grassmannian of the complex associative $3$-planes in $\C^7$, which is the
parametrizing variety of all quaternionic subalgebras of the algebra of complex
octonions $\OO\cong \C^8$. By studying the torus fixed points, we compute the
Poincar\'e polynomial of the compactification.

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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn