For any number field K and genus g ≥ 2, there are infinitely many non-isomorphic hyperelliptic curves over K with Jacobian rank 0, 1, or 2 over K; explicit higher-rank ranges are given for small genera over Q.
Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany Email address:stevangajovic@gmail.com, swpark2008@gmail.com
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
fields
math.NT 1years
2025 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Infinitely many hyperelliptic curves of small genus and small fixed rank, and of any genus and rank two
For any number field K and genus g ≥ 2, there are infinitely many non-isomorphic hyperelliptic curves over K with Jacobian rank 0, 1, or 2 over K; explicit higher-rank ranges are given for small genera over Q.