New York Journal of Mathematics
Volume 14 (2008) 517-538

Volume 14

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Jim Agler, John E. McCarthy, and Mark Stankus

Local geometry of zero sets of holomorphic functions near the torus

Published: October 10, 2008
Keywords: Toral polynomial; locally toral; sidal; locally sidal
Subject: 14J989, 32B99
Abstract
We call a holomorphic function f on a domain in Cn locally toral at the point P in the n-torus if the intersection of the zero set of f with the n-torus has dimension n-1 at P. We study the interplay between the structure of locally toral functions and the geometry of their zero sets.
Acknowledgements

The first author was partially supported by National Science Foundation Grant DMS 0400826
The second author was partially supported by National Science Foundation Grant DMS 0501079
Author information

Jim Agler:
U.C. San Diego, La Jolla, CA 92093
jagler@ucsd.edu

John E. McCarthy:
Washington University, St. Louis, MO 63130
mccarthy@math.wustl.edu

Mark Stankus:
California Polytechnic State University, San Luis Obispo, CA 93407
mstankus@calpoly.edu