Using techniques from the theory of marked bases, we develop new effective methods for detecting and constructing Cohen-Macaulay, Gorenstein and complete intersection homogeneous polynomial ideals over a field K. Due to the functorial properties of marked bases, an elementary proof follows for the openness of the arithmetically Cohen-Macaulay, arithmetically Gorenstein and strict complete intersection K-rational points loci in a Hilbert scheme with a non-constant Hilbert polynomial.
Cohen-Macaulay, Gorenstein and complete intersection conditions by marked bases
Cristina Bertone;
2026-01-01
Abstract
Using techniques from the theory of marked bases, we develop new effective methods for detecting and constructing Cohen-Macaulay, Gorenstein and complete intersection homogeneous polynomial ideals over a field K. Due to the functorial properties of marked bases, an elementary proof follows for the openness of the arithmetically Cohen-Macaulay, arithmetically Gorenstein and strict complete intersection K-rational points loci in a Hilbert scheme with a non-constant Hilbert polynomial.
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