Periods of real biextensions

Hain, Richard

doi:10.2140/ant.2026.20.1855

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-7833 (online)

ISSN 1937-0652 (print)

Author index

To appear

Other MSP journals

Periods of real biextensions

Richard Hain

Vol. 20 (2026), No. 9, 1855–1876

DOI: 10.2140/ant.2026.20.1855

Abstract

A real biextension is a mixed Hodge structure that is an extension of $ℝ$ by a mixed Hodge structure with weights $- 1$ and $- 2$ . It is split if it is a direct sum of its graded quotients. A unipotent real biextension over an algebraic manifold $X$ is a variation of mixed Hodge structure over $X$ , each of whose fibers is a real biextension and whose weight-graded quotients are constant. We show that, if a unipotent real biextension has nonabelian monodromy, then its “general fiber” is not split. This result is a tool for investigating the boundary behaviour of normal functions.

Keywords

biextension, variation of mixed Hodge structure, period mapping

Mathematical Subject Classification

Primary: 14C30

Secondary: 32G20

Milestones

Received: 27 August 2024

Revised: 1 June 2025

Accepted: 5 August 2025

Published: 19 October 2026

Authors

Richard Hain
Department of Mathematics Duke University Durham, NC United States

Open Access made possible by participating institutions via Subscribe to Open.

Vol. 20, No. 9, 2026