Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complex multi-projective variety and entanglement   In this paper, we will show that a vanishing generalized concurrence of a
separable state can be seen as an algebraic variety called the Segre variety.
This variety define a quadric space which gives a geometric picture of
separable states. For pure, bi- and three-partite states the variety equals the
generalized concurrence. Moreover, we generalize the Segre variety to a general
multipartite state by relating to a quadric space defined by two-by-two
subdeterminants.

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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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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: hep-ex
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The categories of this paper are: gr-qc