Integrals of logarithmic forms on semi-algebraic sets and a generalized Cauchy formula Part II: generalized Cauchy formula

TL;DR

This paper extends the generalized Cauchy formula to integrals of logarithmic forms on products of projective lines and applies it to construct Hodge realizations of mixed Tate motives.

Contribution

It introduces a generalized Cauchy formula for logarithmic forms on semi-algebraic sets and applies it to motives, building on previous work in the series.

Findings

Proved a generalized Cauchy formula for logarithmic forms on projective line products.

Applied the formula to construct Hodge realizations of mixed Tate motives.

Extended the theoretical framework for integrals of logarithmic forms in algebraic geometry.

Abstract

This paper is the continuation of the paper arXiv:1509.06950, which is Part I under the same title. In this paper, we prove a generalized Cauchy formula for the integrals of logarithmic forms on products of projective lines, and give an application to the construction of Hodge realization of mixed Tate motives.