Mathematics 533b
Winter 2007
Homework 2.
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 fun
Math 533b, Winter 2007
Introduction to Several Complex Variables
Syllabus
Instructor: Rasul Shakov, MC 112. E-mail: [email protected] (emails will be answered within 48
hours), oce hours TBA.
Textbook:
Mathematics 533b
Winter 2007
Homework 4.
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 =
Mathematics 533b
Winter 2007
Homework 3.
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
Mathematics 533b
Winter 2007
Homework 1.
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 inter