Zariski-Offenheit von eigentlichen, flachen holomorphen Abbildungen.
On the Hardy space of the unit disk, we consider operators which are finite sums of products of a Toeplitz operator and a Hankel operator. We then give characterizations for such operators to be zero. Our results extend several known results using completely different arguments.
We exhibit a class of bounded, strongly convex Hartogs domains with real-analytic boundary which are not Lu Qi-Keng, i.e. whose Bergman kernel function has a zero.
Let be a bounded strictly pseudoconvex domain in and let be a positive divisor of with finite area. We prove that there exists a bounded holomorphic function such that is the zero set of . This result has previously been obtained by Berndtsson in the case where is the unit ball in .
We propose a refinement of the notion of blow-Nash equivalence between Nash function germs, which has been introduced in [2] as an analog in the Nash setting of the blow-analytic equivalence defined by T.-C. Kuo [13]. The new definition is more natural and geometric. Moreover, this equivalence relation still does not admit moduli for a Nash family of isolated singularities. But though the zeta functions constructed in [2] are no longer invariants for this new relation, thanks to a Denef & Loeser...