Effective Bounds of Linear Series on Algebraic Varieties and Arithmetic Varieties

Abstract

In this paper, we prove effective upper bounds for effective sections of line bundles on projective varieties and hermitian line bundles on arithmetic varieties in terms of the volumes. They are effective versions of the Hilbert--Samuel formula and the arithmetic Hilbert--Samuel formula.

References in corpus (3)

• Estimation of arithmetic linear series
• Majorations explicites de fonctions de Hilbert-Samuel géométrique et arithmétique
• Relative Noether inequality on fibered surfaces