Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-05-29T01:03:52.627Z Has data issue: false hasContentIssue false
  • English
  • Français

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, uwen@uni-paderborn.de
Peter Schenzel
Affiliation:
Fachbereich Mathematik und Informatik Martin-Luther-Universität, Halle-Wittenberg, D - 06 099 Halle, Germany, schenzel@mathematik.uni-halle.de
Rights & Permissions [Opens in a new window]

Abstract.

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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