Relative Bogomolov’s inequality and the cone of positive divisors on the moduli space of stable curves

DOI10.1090/S0894-0347-98-00261-6zbMath0893.14004arXivalg-geom/9612011MaRDI QIDQ4396471

Atsushi Moriwaki

Publication date: 14 June 1998

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/alg-geom/9612011

zbMATH Keywords

Chern classBogomolov's inequalitycone of weakly positive Cartier divisorsmoduli space of stable curve

Mathematics Subject Classification ID

Families, moduli of curves (algebraic) (14H10) Characteristic classes and numbers in differential topology (57R20) Divisors, linear systems, invertible sheaves (14C20) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

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Cites Work

• Unnamed Item
• Unnamed Item
• Admissible pairing on a curve
• Théoremes de Bertini et applications
• Fibered algebraic surfaces with low slope
• The theorem of Grauert-Mülich-Spindler
• Stability of projective varieties
• Semi-stability and heights of cycles
• Bogomolov conjecture for curves of genus 2 over function fields
• The irreducibility of the space of curves of a given genus
• Bogomolov conjecture over function fields for stable curves with only irreducible fibers (Version 2.0)
• Divisor classes associated to families of stable varieties, with applications to the moduli space of curves
• On a Theorem of Bogomolov on Chern Classes of Stable Bundles
• The projectivity of the moduli space of stable curves. I: Preliminaries on "det" and "Div".
• A sharp slope inequality for general stable fibrations of curves.
• Stable vector bundles and the frobenius morphism
• Arithmetic Bogomolov-Gieseker's Inequality
• Ample Vector Bundles on Curves