Algebra & Number Theory· 2026Q1
Rational curves and the Hilbert property on Jacobian Kummer varieties
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- Q1SCImago
- 2026year
Short summary
Jacobian Kummer varieties associated with hyperelliptic curves of genus ≥ 3 (and odd degree) and Kummer surfaces of genus 2 curves possess the Hilbert property, confirming a conjecture by Corvaja and Zannier.
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Key points
- Confirms the Corvaja-Zannier conjecture for specific Jacobian Kummer varieties.
- Proves the Hilbert property for Kummer surfaces of genus 2 curves.
- Extends the proof to Jacobian Kummer varieties of hyperelliptic curves with genus ≥ 3 and odd degree.
- Applies to varieties over finitely generated fields of characteristic zero.
AI-generated from the title and abstract; the full text is not read.
Abstract
Let K be a finitely generated field of characteristic zero.A conjecture by Corvaja and Zannier predicts that smooth, projective, simply connected varieties over K with Zariski dense set of rational points have the Hilbert property.We confirm this conjecture for all Kummer surfaces associated to the Jacobian of a genus 2 curve over K, and in general for all Jacobian Kummer varieties associated to a hyperelliptic curve of genus ≥ 3 of odd degree over K.
The authors' abstract, as published at the source. Algebra & Number Theory, 2026 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics