Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Grothendieck-Serre formula and bigraded Cohen-Macaulay Rees algebras   The Grothendieck-Serre formula for the difference between the Hilbert
function and Hilbert polynomial of a graded algebra is generalized for bigraded
standard algebras. This is used to get a similar formula for the difference
between the Bhattacharya function and Bhattacharya polynomial of two m-primary
ideals I and J in a local ring (A,m) in terms of local cohomology modules of
Rees algebras of I and J. The cohomology of a variation of the Kirby-Mehran
complex for bigraded Rees algebras is studied which is used to characterize the
Cohen-Macaulay property of bigraded Rees algebra of I and J for two dimensional
Cohen-Macaulay local rings.

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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an