Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic behaviour of arithmetically Cohen-Macaulay blow-ups   This paper addresses problems related to the existence of arithmetic
Macaulayfications of projective schemes. Let Y be the blow-up of a projective
scheme X = Proj R along the ideal sheaf of I \subset R. It is known that there
are embeddings Y \cong Proj k[(I^e)_c] for c \ge d(I)e + 1, where d(I) denotes
the maximal generating degree of I, and that there exists a Cohen-Macaulay ring
of the form k[(I^e)_c] if and only if H^0(Y,O_Y) = k, H^i(Y,O_Y) = 0 for i =
1,...,dim Y-1, Y is equidimensional and Cohen-Macaulay. Cutkosky and Herzog
asked when there is a linear bound on c and e ensuring that k[(I^e)_c] is a
Cohen-Macaulay ring. We obtain a surprising compelte answer to this question,
namely, that under the above conditions, there are well determined invariants a
and b such that k[(I^e)_c] is Cohen-Macaulay for all c > d(I)e + a and e > b.
Our approach is based on recent results on the asymptotic linearity of the
Castelnuovo-Mumford regularity of ideal powers. We also investigate the
existence of a Cohen-Macaulay Rees algebra of the form R[(I^e)_ct] (which
provides an arithmetic Macaulayfication for X). If R has negative a*-invariant,
we prove that such a Cohen-Macaulay Rees algebra exists if and only if f_*O_Y =
O_X, R^i f*O_Y = 0 for i > 0, Y is equidimensional and Cohen-Macaulay.
Especially, these conditions imply the Cohen-Macaulayness of R[(I^e)_ct] for
all c > d(I)e + a and e > b. The above results can be applied to obtain several
new classes of Cohen-Macaulay algebras.

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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: stat