Skip to main content
×
×
Home

Bounds for the cohomology and the Castelnuovo regularity of certain surfaces

  • M. Brodmann (a1) and W. Vogel (a2)
Extract

Let XP r be a reduced, irreducible and non-degenerate projective variety over an algebraically closed field K of characteristic 0. Let reg(x) be the Castelnuovo-Mumford regularity of the sheaf of ideals associated to X.

Then it is an open problem—due to D. Eisenbud (see e.g. [E-Go])—whether

(0.1) reg(X) ≤ deg(x) - codim (x) + 1,

where deg(x) denotes the degree of X and codim(x) denotes the codimension of X. In many cases, this inequality has been proven to hold true.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Bounds for the cohomology and the Castelnuovo regularity of certain surfaces
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Bounds for the cohomology and the Castelnuovo regularity of certain surfaces
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Bounds for the cohomology and the Castelnuovo regularity of certain surfaces
      Available formats
      ×
Copyright
References
Hide All
[Br] Brodmann, M., Bounds on the cohomological Hilbert functions of a projective variety, J. Algebra, 109 (1987), 352380.
[Br2] Brodmann, M., Sectional genus and cohomology of projective varieties, Math. Zeitschr., 208 (1991) 101126.
[E-Go] Eisenbud, D., Goto, S., Linear resolutions and minimal multiplicity, J. Algebra, 88 (1984), 89133.
[Ev-Gr] Evans, E. G. Jr., Griffiths, P. A., Local cohomology modules for normal domains, J. London Math. Soc., 19 (1979), 277284.
[F-V] Flenner, H., Vogel, W., Connectivity and its Applications to Improper Intersections in P, Math. Gottingensis, Heft 53, Göttingen 1988.
[Fi-V] Fiorentini, M., Vogel, W., Old and New Results and Problems on Buchsbaum Modules, I*, Semin Geom., Univ. Studi Bologna 1988-1991, 5361, Bologna 1991.
[Go] Goto, S., A Note on quasi-Buchsbaum Rings, Proc. Amer. Math. Soc., 90, (1984), 511516.
[G-L-P] Gruson, L., Lazarsfeld, R., Peskine, C., On a theorem of Castelnuovo and the equations defining space curves, Invent. Math., 72 (1983), 491 — 506.
[H] Harris, J., The genus of space curves, Math. Ann., 249 (1980), 191204.
[Ho-M-V] Hoa, T., Miro-Roig, R., Vogel, W., On numerical invariants of locally Cohen-Macaulay Schemes in P n , Preprint, MPI/0-57.
[Ho-St-V] Hoa, T., Stückrad, J., Vogel, W., Towards a structure theory for projective varieties of degree = codimension + 2, J. Pure Appl. Algebra, 71 (1991), 203231.
[Ho-V] Hoa, T., Vogel, W., Castelnuovo-Mumford regularity and hyperplane sections, to appear in Algebra, J..
[L] Lazarsfeld, R., A sharp Castelnuovo bound for smooth surfaces, Duke Math. J., 55 (1987), 423429.
[Mu] Mumford, D., Pathologies III, Amer. J. Math. 89 (1967), 94104.
[Mu2] Mumford, D., Lectures on Curves on an Algebraic Surface, Annals of Math. Studies No 59, Princeton Univ. Press 1966.
[N] Nagel, U., Uber Gradschranken fiir Syzygien and kohomologische Hilbert-funktionen, Diss. Univ. Paderborn, 1990.
[St-V1] Stückrad, J., Vogel, W., Castelnuovo bounds for certain subvarieties of P n , Math. Ann., 276 (1987), 341352.
[St-V2] Stückrad, J., Vogel, W., Castelnuovo’s regularity and cohomological properties of sets of points in P n , Math. Ann., 284 (1989), 487501.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Nagoya Mathematical Journal
  • ISSN: 0027-7630
  • EISSN: 2152-6842
  • URL: /core/journals/nagoya-mathematical-journal
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 12 *
Loading metrics...

Abstract views

Total abstract views: 36 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 20th July 2018. This data will be updated every 24 hours.