Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A vanishing theorem for weight one syzygies   Inspired by the methods of Voisin, the first two authors recently proved that
one could read off the gonality of a curve C from the syzygies of its ideal in
any one embedding of sufficiently large degree. This was deduced from from a
vanishing theorem for the asymptotic syzygies associated to an arbitrary line
bundle B on C. The present paper extends this vanishing theorem to a smooth
projective variety X of arbitrary dimension. Specifically, given a line bundle
B on X, we prove that if B is p-jet very ample (i.e. the sections of B separate
jets of total weight p+1) then the weight one Koszul cohomology group
K_{p,1}(X, B; L) vanishes for all sufficiently positive L. In the other
direction, we show that if there is a reduced cycle of length p+1 that fails to
impose independent conditions on sections of B, then the Koszul group in
question is non-zero for very positive L.

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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys