Deligne-Riemann-Roch Theorems I. Uniqueness of Deligne Pairings and Degree $1$ Part of Deligne-Riemann-Roch Isomorphisms

TL;DR

This paper proves the uniqueness of Deligne pairings and establishes the degree 1 component of the Deligne-Riemann-Roch isomorphisms, laying groundwork for broader applications in algebraic geometry.

Contribution

It introduces a uniqueness theorem for Deligne pairings and proves the degree 1 part of the Deligne-Riemann-Roch theorem, advancing the theoretical framework.

Findings

Proved the uniqueness of Deligne pairings.

Established the degree 1 component of Deligne-Riemann-Roch isomorphisms.

Laid foundation for future generalizations.

Abstract

This is the first of a series of papers. Our final goal is to establish Deligne-Riemann-Roch isomorphisms in various settings. In this paper, we establish a uniqueness theorem for Deligne pairings and prove the degree $1$ part of the Deligne-Riemann-Roch theorem.