Cohen-Macaulay, Gorenstein and complete intersection conditions by marked bases
arXiv:2410.17090 · doi:10.1016/j.jalgebra.2025.11.034
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.
29 pages, comments are welcome