Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Freeness and Minimal Free Resolutions of Modules of Differential
  Operators of a Generic Hyperplane Arrangement   Let A be a generic hyperplane arrangement composed of r hyperplanes in an
n-dimensional vector space, and S the polynomial ring in n variables. We
consider the S-submodule D(m)(A) of the nth Weyl algebra of homogeneous
differential operators of order m preserving the defining ideal of A.
  We prove that if n \geq 3, r > n,m > r - n + 1, then D(m)(A) is free (Holm's
conjecture). Combining this with some results by Holm, we see that D(m)(A) is
free unless n \geq 3, r > n,m < r - n + 1. In the remaining case, we construct
a minimal free resolution of D(m)(A) by generalizing Yuzvinsky's construction
for m = 1. In addition, we construct a minimal free resolution of the transpose
of the m-jet module, which generalizes a result by Rose and Terao for m = 1.

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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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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-th
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org