Castelnuovo–Mumford Regularity of Annihilators, Ext and Tor Modules

  • Markus Brodmann
  • Cao Huy Linh
  • Maria-Helena Seiler


Let R be a Noetherian homogeneous (e.g. standard graded) ring with local Artinian base ring (in degree 0), and let M and N be two finitely generated graded R-modules. We give various upper bounds for the Castelnuovo-Mumford regularity of the annihilator of M and the modules Ext(M,N) and Tor(M,N) in terms of basic invariants of R, M and N.


Characteristic Variety Polynomial Ring Singular Locus Hilbert Function Weyl Algebra 
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The first author expresses his gratitude toward David Eisenbud for the many things he could learn either from David’s published work, David’s conference talks, or from a number of inspiring personal discussions with David, for example, at the Forschungsinstitut Oberwolfach, at Brandeis University, on a mountain walk in les Plans sur Bex, on a Winter excursion to Arosa, and at several other occasions—discussions which were of great influence on the first author’s work. The second author was partially supported by NAFOSTED (Vietnam).


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Markus Brodmann
    • 1
  • Cao Huy Linh
    • 2
  • Maria-Helena Seiler
    • 1
  1. 1.Institut für MathematikUniversität ZürichzürichSwitzerland
  2. 2.Department of MathematicsCollege of Education, Hue UniversityHue CityViet Nam

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