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Degree bounds for generators of cohomology modules and Castelnuovo-Mumford regularity

Published online by Cambridge University Press:  22 January 2016

Uwe Nagel  and
Peter Schenzel
Uwe Nagel
Affiliation:
Fachbereich Mathematik und Informatik Universität-Gesamthochschule Paderborn, D - 33095 Paderborn, Germany, [email protected]
Peter Schenzel
Affiliation:
Fachbereich Mathematik und Informatik Martin-Luther-Universität, Halle-Wittenberg, D - 06 099 Halle, Germany, [email protected]
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Abstract.

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By extending Mumford’s result on the generating by global sections there are estimates on the degree for generators of local cohomology modules. These arguments provide bounds on the Castelnuovo-Mumford regularity, in particular for Cohen-Macaulay varieties. As an application they imply a few more cases of varieties that satisfy a conjecture posed by Eisenbud and Gôto.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 152 , December 1998 , pp. 153 - 174
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1998

References

[1] Ballico, E., On singular curves in positive characteristic, Math. Nachr., 141 (1989), 267–273.CrossRefGoogle Scholar
[2] Bresinsky, H., Curtis, F., Fiorentini, M. and Hoa, L. T., On the structure of local cohomology modules for monomial curves in Nagoya Math. J., 136 (1994), 81–114.CrossRefGoogle Scholar
[3] Brodmann, M. and Nagel, U., Bounding cohomological Hilbert functions by hyper-plane sections, J. Algebra, 174 (1995), 323–348.CrossRefGoogle Scholar
[4] Brodmann, M. and Vogel, W., Bounds for the cohomology and the Castelnuovo regularity of certain surfaces, Nagoya Math. J., 131 (1993), 109–126.CrossRefGoogle Scholar
[5] Eisenbud, D. and Gôto, S., Linear free resolutions and minimal multiplicity, J. Algebra, 88 (1984), 89–133.CrossRefGoogle Scholar
[6] Gruson, L., Lazarsfeld, R. and Peskine, C., On a theorem of Castelnuovo and the equations defining space curves, Invent. Math., 72 (1983), 491–506.CrossRefGoogle Scholar
[7] Hartshorne, R., Algebraic Geometry, Graduate Texts in Math., Springer-Verlag, 1977.CrossRefGoogle Scholar
[8] Hoa, L. T. and Miyazaki, C., Bounds on Castelnuovo-Mumford regularity for generalized Cohen-Macaulay graded rings, Math. Ann., 301 (1995), 587–598.CrossRefGoogle Scholar
[9] Hoa, L. T. and Vogel, W., Castelnuovo-Mumford regularity and hyperplane sections, J. Algebra, 163 (1994), 3 48–365.CrossRefGoogle Scholar
[10] Hochster, M., Contracted ideals from integral extensions of regular rings, Nagoya Math. J., 51 (1973), 25–43.CrossRefGoogle Scholar
[11] Lazarsfeld, R., A sharp Castelnuovo bound for smooth surfaces, Duke Math J., 55 (1987), 423–429.CrossRefGoogle Scholar
[12] Migliore, J. and Miró-Roig, R. M., On k-Buchsbaum curves, Commun. Algebra, 18 (8) (1990), 2403–2422.CrossRefGoogle Scholar
[13] Miyazaki, C., Sharp bounds on Castelnuovo-Mumford regularity Preprint, Nagano National College of Technology, 1997.Google Scholar
[14] Miyazaki, C. and Vogel, W., Bounds on cohomology and Castelnuovo-Mumford regularity, J. Algebra, 185 (1996), 626–642.CrossRefGoogle Scholar
[15] Mumford, D., Lectures on curves on an algebraic surface, 59, Princeton Univ. Press, 1966.CrossRefGoogle Scholar
[16] Mumford, D., Pathologies III, Amer. J. Math., 89 (1967), 94–104.Google Scholar
[17] Nagel, U., Castelnuovo’s regularity and Hilbert functions, Compositio Math., 76 (1990), 265–275.Google Scholar
[18] Nagel, U. and Schenzel, P., Cohomological annihilators and Castelnuovo-Mumford regularity, Contemp. Math., 159 (1994), 307–328.CrossRefGoogle Scholar
[19] Ran, Z., Local differential geometry and generic projections of threefolds, J. Differential Geom., 32 (1990), 131–137.CrossRefGoogle Scholar
[20] Stückrad, J. and Vogel, W., Castelnuovo bounds for certain subvarieties in ℙn , Math. Ann., 276 (1987), 341–352.CrossRefGoogle Scholar