Computation of polarized metrized graph invariants by using discrete Laplacian matrix

DOI10.1090/mcom/2981zbMath1320.05071arXiv1202.4641OpenAlexW2143664499MaRDI QIDQ5501154

Zübeyir Çınkır

Publication date: 13 August 2015

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

Full work available at URL: https://arxiv.org/abs/1202.4641

zbMATH Keywords

relative dualizing sheafmetrized graphtau constantpseudo inversepolarized metrized graphresistance functiondiscrete Laplacian matrixinvariants of polarized metrized graphs

Mathematics Subject Classification ID

Programming involving graphs or networks (90C35) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) [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)] Varieties over global fields (11G35) Heights (11G50) Distance in graphs (05C12) Graph algorithms (graph-theoretic aspects) (05C85) Applications of graph theory to circuits and networks (94C15) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

Related Items (2)

Admissible invariants of genus 3 curves ⋮ On the height of Gross-Schoen cycles in genus three

Uses Software

• Mathematica
• Matlab

Cites Work

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• The tau constant of a metrized graph and its behavior under graph operations
• Admissible pairing on a curve
• Matrix multiplication via arithmetic progressions
• Effective calculation of the geometric height and the Bogomolov conjecture for hyperelliptic curves over function fields
• Bogomolov conjecture for curves of genus 2 over function fields
• Geometric Bogomolov's conjecture for curves of genus 3 over function fields.
• The tau constant and the edge connectivity of a metrized graph
• Zhang's conjecture and the effective Bogomolov conjecture over function fields
• The tau constant and the discrete Laplacian matrix of a metrized graph
• Gaussian elimination is not optimal
• Gross-Schoen cycles and dualising sheaves
• Graph invariants and the positivity of the height of the Gross-Schoen cycle for some curves
• Bogomolov conjecture over function fields for stable curves with only irreducible fibers (Version 2.0)
• The Geometric Bogomolov Conjecture for Curves of Small Genus
• Admissible constants for genus 2 curves
• The capacity pairing.
• Second variation of Zhang’s λ-invariant on the moduli space of curves
• Harmonic Analysis on Metrized Graphs
• Multiplying matrices faster than coppersmith-winograd

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