Hodge structures and Weierstrass $\sigma$-function

TL;DR

This paper introduces a new definition of Hodge structures and demonstrates that real Hodge structures can be characterized by specific operators related to the Weierstrass sigma-function.

Contribution

It provides a novel characterization of -Hodge structures using operators annihilated by the Weierstrass sigma-function, offering a new perspective in Hodge theory.

Findings

-Hodge structures are determined by -linear operators

Operators are characterized by the Weierstrass -function

New framework links Hodge structures with complex analysis

Abstract

In this paper we introduce new definition of Hodge structures and show that $\R$-Hodge structures are determined by $\R$-linear operators that are annihilated by the Weierstrass $\sigma$-function