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arXiv · 2410.17090

Cohen-Macaulay, Gorenstein and complete intersection conditions by marked bases

Cristina Bertone·Francesca Cioffi·Matthias Orth·Werner M. Seiler
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Abstract

Using techniques coming from the theory of marked bases, we develop new computational methods for detection and construction of Cohen-Macaulay, Gorenstein and complete intersection homogeneous polynomial ideals. Thanks to the functorial properties of marked bases, an elementary and effective proof of the openness of arithmetically Cohen-Macaulay, arithmetically Gorenstein and strict complete intersection loci in a Hilbert scheme follows, for a non-constant Hilbert polynomial.

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Cristina Bertone, Francesca Cioffi, Matthias Orth, Werner M. Seiler. 2024-10-22. Cohen-Macaulay, Gorenstein and complete intersection conditions by marked bases. https://doi.org/10.1016/j.jalgebra.2025.11.034

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