We give an algebraic description of (wave) fronts that appear in strictly hyperbolic Cauchy problems. A concrete form of a defining function of the wave front issued from the initial algebraic variety is obtained with the aid of Gauss-Manin systems satisfied by Leray's residues.
@article{bwmeta1.element.bwnjournal-article-apmv74z1p275bwm,
author = {Tanab\'e, Susumu},
title = {Hyperbolic Cauchy problem and Leray's residue formula},
journal = {Annales Polonici Mathematici},
volume = {75},
year = {2000},
pages = {275-290},
zbl = {0964.35091},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv74z1p275bwm}
}
Tanabé, Susumu. Hyperbolic Cauchy problem and Leray's residue formula. Annales Polonici Mathematici, Tome 75 (2000) pp. 275-290. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv74z1p275bwm/
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