Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extensions of the Multiplicity Conjecture   The Multiplicity conjecture of Herzog, Huneke, and Srinivasan states an upper
bound for the multiplicity of any graded $k$-algebra as well as a lower bound
for Cohen-Macaulay algebras. In this note we extend this conjecture in several
directions. We discuss when these bounds are sharp, find a sharp lower bound in
case of not necessarily arithmetically Cohen-Macaulay one-dimensional schemes
of 3-space, and we propose an upper bound for finitely generated graded torsion
modules. We establish this bound for torsion modules whose codimension is at
most two.

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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph