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Dual \(F\)-signature of Cohen-Macaulay modules over rational double points. (English) Zbl 1348.13009

Summary: The dual \(F\)-signature is a numerical invariant defined via the Frobenius morphism in positive characteristic. It is known that the dual \(F\)-signature characterizes some singularities. However, the value of the dual \(F\)-signature is not known except in only a few cases. In this paper, we determine the dual \(F\)-signature of Cohen-Macaulay modules over two-dimensional rational double points. The method for determining the dual \(F\)-signature is also valid for determining the Hilbert-Kunz multiplicity. We discuss it in Appendix.

MSC:

13A35 Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure
13A50 Actions of groups on commutative rings; invariant theory
13C14 Cohen-Macaulay modules
16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
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References:

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