Hodge theory, between algebraicity and transcendence

TL;DR

This paper surveys recent progress in understanding the transcendental aspects of Hodge theory for complex algebraic varieties, highlighting the role of o-minimal geometry in bounding transcendence.

Contribution

It introduces o-minimal geometry as a framework to bound transcendence in Hodge theory, connecting algebraic and transcendental structures.

Findings

O-minimal geometry provides new bounds on transcendence in Hodge theory.

Recent advances link algebraic structures with transcendental properties.

The survey highlights the role of o-minimal methods in Hodge theory.

Abstract

The Hodge theory of complex algebraic varieties is at heart a transcendental comparison of two algebraic structures. We survey the recent advances bounding this transcendence, mainly due to the introduction of o- minimal geometry as a natural framework for Hodge theory.