Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Expected centre of mass of the random Kodaira embedding   Let $X \subset \mathbb{P}^{N-1}$ be a smooth projective variety. To each $g
\in SL (N , \mathbb{C})$ which induces the embedding $g \cdot X \subset
\mathbb{P}^{N-1}$ given by the ambient linear action we can associate a matrix
$\bar{\mu}_X (g)$ called the centre of mass, which depends nonlinearly on $g$.
With respect to the probability measure on $SL (N , \mathbb{C})$ induced by the
Haar measure and the Gaussian unitary ensemble, we prove that the expectation
of the centre of mass is a constant multiple of the identity matrix for any
smooth projective variety.

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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol