2022/06/16 by Dorian Ni, Ni, Dorian
Physics and Astronomy · #11G50 (Secondary) #14G40 (Primary) #Advanced Differential Geometry Research #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2206.07954
openalex publication_date 2022/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present an Arakelov theoretic version of the deformation to the normal cone. In particular, the geometric data is enriched with a deformation of a Hermitian line bundle. We introduce numerical invariants called arithmetic Hilbert invariants and prove the conservation of these invariants along the deformation. In a following article, this conservation of number theorem will allow a demonstration of the arithmetic Hilbert-Samuel theorem.