Maciej Denkowski

Title: On the Kuratowski convergence and algebraicity

Abstract: 
After a short introduction on the Kuratowski convergence in complex 
analytic geometry we will show how it can be used to obtain some 
algebraicity criteria for globally analytic sets. To this aim we will 
introduce a notion of global degree of an analytic set, as well as a 
degree of Nash sets. The uniform boundedness of the latter for a 
convergent sequence of Nash sets permits to conclude that the limit 
is Nash, too (this is a counterpart for Nash sets of the algebraic 
Twozewski-Winiarski Theorem based itself on the Bishop Theorem).  
As a by-product we will also present a Chevalley-Remmert Projection 
Theorem for Nash sets. The talk is based on a joint work with Rafał 
Pierzchała.