Computing period matrices and the Abel-Jacobi map of superelliptic curves

DOI10.1090/mcom/3351zbMath1437.14060arXiv1707.07249OpenAlexW4289039381MaRDI QIDQ4561377

Pascal Molin, Christian Neurohr

Publication date: 5 December 2018

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.07249

zbMATH Keywords

complexityalgorithmnumerical integrationperiod matrixAbel-Jacobi mapsuperelliptic curves

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Computational aspects of algebraic curves (14Q05) [https://portal.mardi4nfdi.de/w/index.php?title=+Special%3ASearch&search=%22Curves+of+arbitrary+genus+or+genus+%28%0D%0Ae+1%29+over+global+fields%22&go=Go Curves of arbitrary genus or genus ( e 1) over global fields (11G30)] Numerical integration (65D30) Analytic computations (11Y35)

Related Items (7)

Numerical computation of endomorphism rings of Jacobians ⋮ Rigorous computation of the endomorphism ring of a Jacobian ⋮ Convergence of discrete period matrices and discrete holomorphic integrals for ramified coverings of the Riemann sphere ⋮ Explicit arithmetic intersection theory and computation of Néron-Tate heights ⋮ Restrictions on endomorphism rings of Jacobians and their minimal fields of definition ⋮ Gluing curves of genus 1 and 2 along their 2-torsion ⋮ Counting points on superelliptic curves in average polynomial time

Uses Software

• Magma
• LMFDB
• Arb
• hcperiods
• endomorphisms
• curve_reconstruction

Cites Work

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• Combinatorial group theory, Riemann surfaces and differential equations
• Computing with the analytic Jacobian of a genus 2 curve
• Equations for the Jacobian of a hyperelliptic curve
• Rigorous computation of the endomorphism ring of a Jacobian
• Weierstrass points on cyclic covers of the projective line
• Plane quartics over $\mathbb {Q}$ with complex multiplication
• Error Estimates for Gauss Quadrature Formulas for Analytic Functions
• On holomorphic differentials of some algebraic function field of one variable over C
• Computing Riemann matrices of algebraic curves

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