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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On support varieties for modules over complete intersections


Author: Petter Andreas Bergh
Journal: Proc. Amer. Math. Soc. 135 (2007), 3795-3803
MSC (2000): Primary 13C14, 13C40, 13D07, 14M10; Secondary 20J06
Published electronically: September 7, 2007
MathSciNet review: 2341929
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Abstract: Let $ (A, \mathfrak{m}, k)$ be a complete intersection of codimension $ c$, and let $ \tilde{k}$ be the algebraic closure of $ k$. We show that every homogeneous algebraic subset of $ \tilde{k}^c$ is the cohomological support variety of an $ A$-module, and that the projective variety of a complete indecomposable maximal Cohen-Macaulay $ A$-module is connected.


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Additional Information

Petter Andreas Bergh
Affiliation: Institutt for matematiske fag, NTNU, N-7491 Trondheim, Norway
Email: bergh@math.ntnu.no

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09009-0
PII: S 0002-9939(07)09009-0
Keywords: Complete intersections, support varieties.
Received by editor(s): June 13, 2006
Received by editor(s) in revised form: September 26, 2006
Published electronically: September 7, 2007
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.