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arXiv · 2405.13829

Iarrobino's symmetric decomposition for self-dual modules

Maciej Wojtala
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Abstract

We generalize Iarrobino's symmetric decomposition for the associated graded algebra of an Artinian Gorenstein algebra to a symmetric decomposition of finite-length self-dual modules over a local algebra, and we deduce consequences for the Hilbert functions of such self-dual modules. We classify the local Hilbert functions for small degree modules. We generalize Kunte's criterion for self-duality in terms of Macaulay's inverse systems.

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Maciej Wojtala. 2024-05-22. Iarrobino's symmetric decomposition for self-dual modules. https://arxiv.org/abs/2405.13829

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