Noncommutative geometry of elliptic surfaces
Algebraic Geometry
2024-04-29 v2 Number Theory
Operator Algebras
Abstract
We recast elliptic surfaces over the projective line in terms of the non-commutative tori and one-parameter families of the periodic continued fractions. The correspondence is used to study the Picard numbers, the ranks and the minimal models of such surfaces. As an example, we calculate the Picard numbers of elliptic surfaces with fibers having complex multiplication.
Cite
@article{arxiv.2106.11392,
title = {Noncommutative geometry of elliptic surfaces},
author = {Igor Nikolaev},
journal= {arXiv preprint arXiv:2106.11392},
year = {2024}
}
Comments
an update