Year: 2022
Type: preprint
Abstract: We give a new proof the arithmetic Hilbert-Samuel theorem by using classical reductions in the theory of coherent sheaves, a direct proof in the case of the projective space and the conservation of some numerical invariants, called arithmetic Hilbert invariants, through the deformation to the projective completion of the cone. This construction lies at the intersection of deformation theory and Arakelov geometry. It provides a deformation of a Hermitian line bundle over the deformation to the normal cone.
Source: arXiv (Cornell University)
Author: Ni, Dorian
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4285429086