English

The classification of ACM curves on a surface in $\mathbb{P}^{3}$

Algebraic Geometry 2026-02-09 v1

Abstract

We classify ACM curves contained in a surface of degree d in P3\mathbb{P}^{3} in terms of weak admissible pairs. In the case of a very general smooth determinantal quartic surface, we provide a geometric description of these curves and compute their Picard classes on the surface. Finally, we present a generalization to ACM closed subvarieties of codimension 11 on a hypersurface in Pn\mathbb{P}^{n}.

Keywords

Cite

@article{arxiv.2602.06141,
  title  = {The classification of ACM curves on a surface in $\mathbb{P}^{3}$},
  author = {Abel Castorena and Montserrat Vite},
  journal= {arXiv preprint arXiv:2602.06141},
  year   = {2026}
}