2012/11/29 by Yuuki Tadokoro, Tadokoro, Yuuki
Computer Science · Mathematics · #14H30 #14H50 #32G20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #math.AG #math.GT #msc:14H30 #msc:14H50 #msc:32G20
paper · pdf · doi:10.48550/arxiv.1211.6910
18 pages, 10 figures
openalex publication_date 2012/11/29 · arxiv created 2014/12/11 · arxiv updated 2014/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A geometric algorithm is introduced for finding a symplectic basis of the first integral homology group of a compact Riemann surface, which is a p-cyclic covering of \mathbb C P1 branched over 3 points. The algorithm yields a previously unknown symplectic basis of the hyperelliptic curve defined by the affine equation w2=z2g+1-1 for genus g≥ 2. We then explicitly obtain the period matrix of this curve, its entries being elements of the (2g+1)-st cyclotomic field. In the proof, the details of our algorithm play no significant role.