Polynomial bounds for Arakelov invariants of Belyi curves. With an appendix by Peter Bruin.

DOI10.2140/ant.2014.8.89zbMath1371.14030arXiv1403.6404OpenAlexW2038653008MaRDI QIDQ2509394

Ariyan Javanpeykar

Publication date: 27 July 2014

Published in: Algebra \& Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.6404

zbMATH Keywords

Riemann surfacesbranched coverscurvesdiscriminantArakelov theoryFaltings heightarithmetic surfacesArakelov invariantsArakelov-Green functionsBelyi degreefaltings' delta invariantself-intersection of the dualising sheafWronskian differential

Mathematics Subject Classification ID

[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)] Heights (11G50) Riemann surfaces; Weierstrass points; gap sequences (14H55) Arithmetic varieties and schemes; Arakelov theory; heights (14G40) Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems (37P30) Arithmetic aspects of dessins d'enfants, Bely? theory (11G32) Dessins d'enfants theory (14H57)

Related Items (11)

Uniform Sup-Norm Bounds on Average for Cusp Forms of Higher Weights ⋮ The minimal regular model of a Fermat curve of odd squarefree exponent and its dualizing sheaf ⋮ New explicit formulas for Faltings' delta-invariant ⋮ On the sharp lower bounds of modular invariants and fractional Dehn twist coefficients ⋮ Calculating and drawing Belyi pairs ⋮ An effective Arakelov-theoretic version of the hyperbolic isogeny theorem ⋮ Semi-stable models of modular curves \(X_0(p^2)\) and some arithmetic applications ⋮ The Belyi degree of a curve is computable ⋮ The effective Shafarevich conjecture for abelian varieties of -type ⋮ Effective sup-norm bounds on average for cusp forms of even weight ⋮ Bounds for Green's functions on noncompact hyperbolic Riemann orbisurfaces of finite volume

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