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  n-dimensional space, Poincare's theorem: the polydisc and the complex ball are not biholomorphic.

 

 

Inhomogeneous Cauchy-Riemann equations in one and several variables, Pompeiu's formula, Dolbeault-Grothendieck theorem, Hartogs' theorem on removability of compact singularities, Dolbeault cohomology groups, Dolbeault's theorem on the polydisc .  

 

 

Domains of holomorphy, holomorphic convexity, Cartan-Thullen theorem, regions of convergence of power series .

 

Approximation theorems in one and several variables, polynomial polyhedrons, Oka-Weil theorem .

literature

 

form of tuition

Lectures

mode of assessment

oral exam