Skip to main content
×
×
Home

Characteristic-free bounds for the Castelnuovo–Mumford regularity

  • Giulio Caviglia (a1) and Enrico Sbarra (a2)
Abstract

We study bounds for the Castelnuovo–Mumford regularity of homogeneous ideals in a polynomial ring in terms of the number of variables and the degree of the generators. In particular, our aim is to give a positive answer to a question posed by Bayer and Mumford in What can be computed in algebraic geometry? (Computational algebraic geometry and commutative algebra, Symposia Mathematica, vol. XXXIV (1993), 1–48) by showing that the known upper bound in characteristic zero holds true also in positive characteristic. We first analyse Giusti's proof, which provides the result in characteristic zero, giving some insight into the combinatorial properties needed in that context. For the general case, we provide a new argument which employs the Bayer–Stillman criterion for detecting regularity.

    • 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.

      Characteristic-free bounds for the Castelnuovo–Mumford regularity
      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.

      Characteristic-free bounds for the Castelnuovo–Mumford regularity
      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.

      Characteristic-free bounds for the Castelnuovo–Mumford regularity
      Available formats
      ×
Copyright
Recommend this journal

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

Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 35 *
Loading metrics...

Abstract views

Total abstract views: 115 *
Loading metrics...

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