Browsing by Author "Çinkir, Zübeyir"

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    Admissible invariants of genus 3 curves
    (Springer New York LLC, 2015) Cinkir, Zubeyir; AGÜ, Mühendislik Fakültesi, Endüstri Mühendisliği Bölümü; Çinkir, Zübeyir
    Several invariants of polarized metrized graphs and their applications in Arithmetic Geometry are studied recently. In this paper, we explicitly calculated these admissible invariants for all curves of genus 3. We find the sharp lower bound for the invariants φ, λ and ε for all polarized metrized graphs of genus 3. This improves the lower bound given for Effective Bogomolov Conjecture for such curves.
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    Article
    Computation of polarized metrized graph invariants by using discrete laplacian matrix
    (American Mathematical Society, 2015) Çinkir. Zübeyir; AGÜ, Mühendislik Fakültesi, Endüstri Mühendisliği Bölümü; Çinkir, Zübeyir
    Several invariants of polarized metrized graphs and their applications in Arithmetic Geometry have been studied recently. In this paper, we give fast algorithms to compute these invariants by expressing them in terms of the discrete Laplacian matrix and its pseudo inverse. The algorithm we give can be used for both symbolic and numerical computations. We present various examples to illustrate the implementation of these algorithms.