A note on the Nullstellensatz for c-holomorphic functions
Volume 90 / 2007
Annales Polonici Mathematici 90 (2007), 219-228 MSC: 32B15, 32A17. DOI: 10.4064/ap90-3-3
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 P/loski–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.