English

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

Commutative Algebra 2026-02-16 v1 Algebraic Geometry

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.

Keywords

Cite

@article{arxiv.2410.17090,
  title  = {Cohen-Macaulay, Gorenstein and complete intersection conditions by marked bases},
  author = {Cristina Bertone and Francesca Cioffi and Matthias Orth and Werner M. Seiler},
  journal= {arXiv preprint arXiv:2410.17090},
  year   = {2026}
}

Comments

29 pages, comments are welcome