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Module Varieties over Canonical Algebras

✍ Scribed by M Barot; Jan Schröer

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
180 KB
Volume
246
Category
Article
ISSN
0021-8693

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✦ Synopsis

The main purpose of this paper is the study of module varieties over the class of canonical algebras, providing a rich source of examples of varieties with interesting properties. Our main tool is a stratification of module varieties, which was recently introduced by Richmond. This stratification does not require a precise knowledge of the module category. If it is finite, then it provides a method to classify irreducible components. We determine the canonical algebras for which this stratification is finite. In this case, we describe the algorithm for calculating the dimension of the variety and the number of irreducible components of maximal dimension. For an infinite family of examples we give easy combinatorial criteria for irreducibility, Cohen-Macaulay and normality.

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