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 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 on a hypersurface in .
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}
}