Hasse principle violation for algebraic families of del Pezzo surfaces of degree 4 and hyperelliptic curves of genus congruent to 1 modulo 4
Abstract
Let g be a positive integer congruent to 1 modulo 4 and K be an arbitrary number field. We construct infinitely many explicit one-parameter algebraic families of degree 4 del Pezzo surfaces and of genus g hyperelliptic curves such that each K-member of the families violates the Hasse principle. In particular, we obtain algebraic families of non-trivial 2-torsion elements in the Tate-Shafarevich group of elliptic curves over K. These Hasse principle violations are explained by the Brauer-Manin obstruction.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
North African History and Literature
Publication details
- Journal / source
- Journal of Algebra
- Publisher
- Elsevier BV
- Volume
- 713
- Pages
- 106–140
- Publication date
- 11 August 2026
- Language
- EN