A new class of surfaces with maximal Picard number

TL;DR

This paper introduces a novel class of algebraic surfaces characterized by maximal Picard number, constructed via Jacobian fibrations related to elliptic modular surfaces, expanding the known examples in algebraic geometry.

Contribution

It constructs new surfaces with maximal Picard number using Jacobian fibrations linked to elliptic modular surfaces, providing explicit examples and methods.

Findings

Surfaces with maximal Picard number are explicitly constructed.

Jacobian fibrations are isogenous to fiber products of elliptic modular surfaces.

New classes of algebraic surfaces are identified with specific geometric properties.

Abstract

A new class of examples of surfaces with maximal Picard number is constructed. These carry pencils of genus two or three curves such their Jacobian fibrations are isogenous to fibre products of elliptic modular surfaces.