The theta invariants and the volume function on arithmetic varieties

2022/02/18 by Mounir Hajli, Hajli, Mounir
Mathematics · Social Sciences · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Vietnamese History and Culture Studies

paper · pdf · doi:10.48550/arxiv.2202.09397

openalex publication_date 2022/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a new arithmetic invariant for hermitian line bundles on an arithmetic variety. We use this invariant to measure the variation of the volume function with respect to the metric. The main result of this paper is a generalized Hodge index theorem on arithmetic toric varieties.

Related

• The arithmetic volume of hypersurfaces in toric varieties and Mahler measures
• Continuity of volumes on arithmetic varieties
• Volume arithmétique de certains fibrés en droites hermitiens sur une variété torique lisse
• Theta invariants of euclidean lattices and infinite-dimensional hermitian vector bundles over arithmetic curves
• The arithmetic Hodge index theorem for adelic line bundles I