Higher order Petri Loci
Abstract
Denote by ${\mathcal P}_{g,d}^{r,k}$ the subset of the moduli space of curves of genus g consisting of those curves that have a linear series of degree d and dimension r for which the Petri map has kernel of dimension at least k. We show the existence of codimension k components of ${\mathcal P}_{g,d}^{r,k}$.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Commutative Algebra and Its Applications
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 11 January 2026
- Document type
- Preprint