The classification of ACM curves on a surface in $\mathbb{P}^{3}$
Abstract
We classify ACM curves contained in a surface of degree d in $\mathbb{P}^{3}$ 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 $1$ on a hypersurface in $\mathbb{P}^{n}$.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Commutative Algebra and Its Applications
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 5 February 2026
- Document type
- Preprint