A note on the Nullstellensatz for c-holomorphic functions

Maciej P. Denkowski¹

¹ Institute of Mathematics Jagiellonian University Reymonta 4 30-059 Kraków, Poland and Institut de Mathématiques de Bordeaux Université Bordeaux 1 351, cours de la Libération 33405 Talence, France

Annales Polonici Mathematici, Tome 90 (2007) no. 3, pp. 219-228

Résumé

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.

Détail

DOI : 10.4064/ap90-3-3

Mots-clés : begin article graph theorem kind nullstellensatz weakly holomorphic functions yields general nullstellensatz c holomorphic functions locally irreducible sets section methods loski tworzewski permit prove effective nullstellensatz c holomorphic functions proper intersection degree intersection cycle exponent extend result isolated improper intersection generalizing result cygan section devoted considerations dimension zero sets c holomorphic mappings