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On Canonical Modules of Toric Face Rings

Published online by Cambridge University Press:  11 January 2016

Bogdan Ichim  and
Tim Römer
Bogdan Ichim
Affiliation:
Universität Osnabrück, FB Mathematik/Informatik, 49069 Osnabrück, Germany Institute of Mathematics, C.P. 1-764, 70700 Bucharest, Romania, bogdan.ichim@math.uos.de, bogdan.ichim@imar.ro
Tim Römer
Affiliation:
Universität Osnabrück, FB Mathematik/Informatik, 49069 Osnabrück, Germany, troemer@uos.de
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Abstract

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Generalizing the concepts of Stanley-Reisner and affine monoid algebras, one can associate to a rational pointed fan Σ in ℝd the ℤd-graded toric face ring K[Σ]. Assuming that K[Σ] is Cohen-Macaulay, the main result of this paper is to characterize the situation when its canonical module is isomorphic to a ℤd-graded ideal of K[Σ]. From this result several algebraic and combinatorial consequences are deduced. As an application, we give a relation between the cleanness of K[Σ] and the shellability of Σ.

Keywords

13C1413D4505E99
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 194 , 2009 , pp. 69 - 90
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2009

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