On the p-rank of singular curves and their smooth models
Finite Fields and their Applications, vol.103, 2025 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 103
- Publication Date: 2025
- Doi Number: 10.1016/j.ffa.2025.102578
- Journal Name: Finite Fields and their Applications
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, MathSciNet, zbMATH
- Keywords: Complete intersections, Jacobian, p-rank
- Middle East Technical University Affiliated: Yes
Abstract
In this paper, we are concerned with the computation of the p-rank and a-number of singular curves and their smooth models. We consider a pair X,X′ of proper curves over an algebraically closed field k of characteristic p, where X′ is a singular curve which lies on a smooth projective variety, particularly on smooth projective surfaces S (with pg(S)=0=q(S)) and X is the smooth model of X′. We determine the p-rank of X by using the exact sequence of group schemes relating the Jacobians JX and JX′. As an application, we determine a relation about the fundamental invariants p-rank and a-number of a family of singular curves and their smooth models. Moreover, we calculate a-number and find lower bound for p-rank of a family of smooth curves.