Pure and Applied Mathematics Quarterly

Volume 19 (2023)

Number 6

Special Issue in honor of Professor Blaine Lawson’s 80th birthday

Guest Editors: Shiu-Yuen Cheng, Paulo Lima-Filho, and Stephen Shing-Toung Yau

Global behavior at infinity of period mappings defined on algebraic surface

Pages: 3035 – 3073

DOI: https://dx.doi.org/10.4310/PAMQ.2023.v19.n6.a16

Authors

Mark Green (Department of Mathematics, University of California, Los Angeles, Calif., U.S.A.)

Phillip Griffiths (Institute for Advanced Study, Princeton, New Jersey, U.S.A.)

Abstract

The global behavior of period mappings defined on generally non-complete algebraic varieties $B$ as well as their local behavior around points in the boundary $Z = \overline{B}\setminus B$ of smooth completions of $B$ have been extensively investigated. In this paper we shall study the global behavior of period mappings in neighborhoods of the entire boundary $Z$ when $\dim B = 2$. One method will be to decompose the dual graph of the boundary into basic building blocks of cycles and trees and analyze these separately. A main tool will be a global version of the classical nilpotent orbit theorem of Schmid.

Received 5 February 2022

Received revised 6 October 2023

Accepted 12 October 2023

Published 30 January 2024