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arXiv · 1311.5963

Generalized F-signature of invariant subrings

Mitsuyasu Hashimoto·Yusuke Nakajima
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Abstract

It is known that a certain invariant subring $R$ has finite $F$-representation type. Thus, we can write the $R$-module ${}^eR$ as a finite direct sum of finitely many $R$-modules. In such a decomposition of ${}^eR$, we pay attention to the multiplicity of each direct summand. For the multiplicity of free direct summand, there is the notion of $F$-signature defined by C. Huneke and G. Leuschke and it characterizes some singularities. In this paper, we extend this notion to non free direct summands and determine the explicit values of them.

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Mitsuyasu Hashimoto, Yusuke Nakajima. 2013-11-23. Generalized F-signature of invariant subrings. https://arxiv.org/abs/1311.5963

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