We begin this article with a graph theorem and a kind of Nullstellensatz for weakly holomorphic functions. This yields a general Nullstellensatz for c-holomorphic functions on locally irreducible sets. In Section 2 some methods of Płoski-Tworzewski permit us to prove an effective Nullstellensatz for c-holomorphic functions in the case of a proper intersection with the degree of the intersection cycle as exponent. We also extend this result to the case of isolated improper intersection, generalizing a result of E. Cygan. The last section is devoted to some considerations on the dimension of the zero-sets of c-holomorphic mappings.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap90-3-3,
author = {Maciej P. Denkowski},
title = {A note on the Nullstellensatz for c-holomorphic functions},
journal = {Annales Polonici Mathematici},
volume = {92},
year = {2007},
pages = {219-228},
zbl = {1121.32003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap90-3-3}
}
Maciej P. Denkowski. A note on the Nullstellensatz for c-holomorphic functions. Annales Polonici Mathematici, Tome 92 (2007) pp. 219-228. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap90-3-3/