discipline 
Mathematics

subject 
Several complex
variables

lecturers 
Róbert Szőke 
credits 
2 
period 
third semester 
curriculum 
Holomorphic functions and maps: complex
differentiability, Cauchy formula, power series in
several variables; Reinhardt domains. Weierstrass preparation and division theorem, the ring of
germs of holomorphic functions at 0 is UFD and Noetherian. Hartogs' theorem on
separate analyticity. Biholomorphic maps: complex norms, maximum principle, Schwarz lemma for normed spaces, automorphisms of
the complex ndimensional space, Poincare's theorem: the polydisc
and the complex ball are not biholomorphic. Inhomogeneous
CauchyRiemann equations in one and several
variables, Pompeiu's formula, DolbeaultGrothendieck
theorem, Hartogs' theorem on removability
of compact singularities, Dolbeault cohomology groups, Dolbeault's
theorem on the polydisc . Domains
of holomorphy, holomorphic
convexity, CartanThullen theorem, regions of
convergence of power series . Approximation
theorems in one and several variables, polynomial polyhedrons, OkaWeil theorem . 
literature 

form of tuition 
Lectures 
mode of assessment 
oral exam 