Generically τ-regular irreducible components of module varieties

2025/02/19 by Bobiński, Grzegorz, Schröer, Jan
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2502.13709

Abstract

In the representation theory of finite-dimensional algebras, the study of projective presentations of maximal rank is closely related to the study of generically τ-regular irreducible components of varieties of modules over such algebras. We show that a module is τ-regular if and only if its minimal projective presentation is of maximal rank. This is a refinement of a theorem by Plamondon. We prove that generic extensions of generically τ-regular components by simple projective modules are again generically τ-regular. This leads to the classification of all generically τ-regular components for triangular algebras. We also show that an algebra is hereditary if and only if all irreducible components of its varieties of modules are generically τ-regular. Finally, we discuss when the set of generically τ-regular components coincides with the set of generically τ^--regular components.

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