Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tensor product surfaces and linear syzygies   Let U be a basepoint free four-dimensional subpace of the space of sections
of bidegree (a,b) on X = P^1 x P^1, with a and b at least 2. The sections
corresponding to U determine a regular map from X to P^3. We show that there
can be at most one linear syzygy on the associated bigraded ideal I_U in the
bigraded ring k[s,t;u,v]. Existence of a linear syzygy, coupled with the
assumption that U is basepoint free, implies the existence of an additional
"special pair" of minimal first syzygies. Using results of Botbol, we show that
these three syzygies are sufficient to determine the implicit equation of the
image of X in P^3; we also show that the singular locus must contain a line.

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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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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: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: astro-ph