Due February 19.
1. Let C be the sheaf of germs of C -smooth functions on R, dened exactly as O by replacing
germs of holomorphic functions with germs of C functions. Dene the topology on C the same
way as for O. P
Math 533b, Winter 2007
Introduction to Several Complex Variables
Instructor: Rasul Shakov, MC 112. E-mail: [email protected] (emails will be answered within 48
hours), oce hours TBA.
Textbook: R. Narasimhan Several Complex Variables, The University
Due March 26.
1. Let f (z) be a holomorphic function in Cn , and let A = cfw_z Cn : f (z) = 0 = . Prove that A
can be compact if and only if n = 1.
2. Let B1 = cfw_(z Cn : |z| < 1 and B2 = cfw_(z Cn : |z| < 1/2. Su
Due March 12.
1. A topological manifold is called a complex manifold of (complex) dimension n, if there exists an
atlas cfw_(U , ), of homeomorphisms : U P n , where U is a coordinate neighbourhood
and P n Cn is t
Due February 5.
1. A complex line in Cn is a subset of the form
cfw_z Cn : z = A + B, C
for some A, B Cn . Prove that two dierent complex lines in C2 can intersect at most at one
2. Let f : Cn C be a continu