Monodromies of singularities of the Hadamard and eñe product

Abstract: We prove that singularities with holomorphic monodromies are preserved by the Hadamard product. We find an explicit formula for the monodromy of the singularities, and similar formulas for the exponential e~ne product. Using these formulas we get new direct proofs of classical results and the invariance of some rings of functions by Hadamard and e~ne product (which is the product of the big Witt ring). This explains the good behavior of the e~ne product on divisors.