English

A local study of the fiber-full scheme

Algebraic Geometry 2023-10-10 v4 Commutative Algebra

Abstract

We study some of the local properties of the fiber-full scheme, which is a fine moduli space that generalizes the Hilbert scheme by parametrizing closed subschemes with prescribed cohomological data. As a consequence, we provide sufficient conditions for cohomology to remain constant under Gr\"obner degenerations. We also describe a tangent-obstruction theory for the fiber-full scheme in analogy with the one for the Hilbert scheme.

Keywords

Cite

@article{arxiv.2202.06652,
  title  = {A local study of the fiber-full scheme},
  author = {Yairon Cid-Ruiz and Ritvik Ramkumar},
  journal= {arXiv preprint arXiv:2202.06652},
  year   = {2023}
}

Comments

to appear in Journal of Algebra