New explicit formulas for Faltings' delta-invariant

DOI10.1007/s00222-016-0713-1zbMath1390.14073arXiv1605.00847OpenAlexW2346228200MaRDI QIDQ2407538

Robert Wilms

Publication date: 6 October 2017

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.00847

zbMATH Keywords

Green functionArakelov theoryarithmetic surfacesFaltings' delta invariant

Mathematics Subject Classification ID

Theta functions and abelian varieties (14K25) [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)] Riemann surfaces; Weierstrass points; gap sequences (14H55) Arithmetic varieties and schemes; Arakelov theory; heights (14G40) Theta functions and curves; Schottky problem (14H42)

Related Items (8)

The genus two free boson in Arakelov geometry ⋮ On arithmetic intersection numbers on self-products of curves ⋮ On the sharp lower bounds of modular invariants and fractional Dehn twist coefficients ⋮ Tropical moments of tropical Jacobians ⋮ Jumps in the height of the Ceresa cycle ⋮ Heights on squares of modular curves ⋮ On CM points away from the Torelli locus ⋮ Néron-Tate heights of cycles on jacobians

Cites Work

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• Asymptotic behavior of the Kawazumi-Zhang invariant for degenerating Riemann surfaces
• Calculus on arithmetic surfaces
• Explicit Mumford isomorphism for hyperelliptic curves
• Theta functions on the theta divisor
• Asymptotic behavior of Faltings's delta function
• The asymptotics of the Arakelov-Green's function and Faltings' delta invariant
• Tata lectures on theta. I: Introduction and motivation: Theta functions in one variable. Basic results on theta functions in several variables. With the assistance of C. Musili, M. Nori, E. Previato, and M. Stillman
• Jacobian nullwerte and algebraic equations
• Bounds on Faltings's delta function through covers
• On the Arakelov geometry of moduli spaces of curves
• Polynomial bounds for Arakelov invariants of Belyi curves. With an appendix by Peter Bruin.
• Harmonic analysis and theta-functions
• Arakelov invariants of Riemann surfaces
• Gross-Schoen cycles and dualising sheaves
• Integral points on moduli schemes of elliptic curves
• Torus bundles and 2-forms on the universal family of Riemann surfaces
• Computational Aspects of Modular Forms and Galois Representations
• On Szpiro's Discriminant Conjecture
• Fibrés d'intersections et intégrales de classes de Chern
• Gauss map on the theta divisor and Green's functions
• INTERSECTION THEORY OF DIVISORS ON AN ARITHMETIC SURFACE
• Two Theorems on the Mapping Class Group of a Surface
• Analytic invariants in Arakelov theory for curves
• On the Discriminant of a Hyperelliptic Curve
• Mapping Class Groups and Moduli Spaces of Curves
• Second variation of Zhang’s λ-invariant on the moduli space of curves
• Bounds on canonical Green's functions
• Faltings’ Delta-Invariant of a Hyperelliptic Riemann Surface
• Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura
• An introduction to Riemann surfaces, algebraic curves and moduli spaces
• A theta lift representation for the Kawazumi-Zhang and Faltings invariants of genus-two Riemann surfaces

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