For Jacobians of genus-2 curves on a K3 surface over number field k, there is a finite extension l/k with infinitely many fibers where the rank jumps, and under extra geometric conditions this holds on a non-thin set.
On special algebraic K3 surfaces. I
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
fields
math.AG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Rank jumps for Jacobians of Hyperelliptic curves on K3 surfaces
For Jacobians of genus-2 curves on a K3 surface over number field k, there is a finite extension l/k with infinitely many fibers where the rank jumps, and under extra geometric conditions this holds on a non-thin set.