Sebastian Casalaina

Functions of a Complex Variable 2

MATH 6360 Fall 2019

Course description

Complex algebraic geometry. Prerequisites: MATH 6350 (Functions of a Complex Variable 1).

Students are strongly encouraged to take Zheng Zhang's course MATH 8174 Topics in Algebra, which will be covering K3 surfaces.


MWF 1:00 PM -- 1:50 PM, MATH 220

University of Colorado Academic Calendar

Office hours

Friday 11:00 AM -- 12:50 PM or by appointment


  1. D. Huybrechts, Complex Geometry: an introduction, Springer 2005, available in .pdf for free from the library.
  2. Our treatment may also follow parts of:

  3. P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley 1978.
  4. C. Voisin, Hodge Theory and Complex Algebraic Geometry, I, Cambridge 2002.
  5. R. Wells, Differential Analysis on Complex Manifolds (Third Edition), Springer 2008.
  6. D. Arapura, Algebraic Geometry over the Complex Numbers, Springer 2012.
  7. We wil also use the following as a references occasionally:

  8. R. Gunning and H. Rossi, Analytic Functions of Several Complex Variables , Prentice--Hall 1965.
  9. A. Browder, Mathematical Analysis: an introduction, Springer 1996.
  10. P. Aluffi, Algebra: chapter 0, Graduate Studies in Math., AMS, 2009.
  11. R. Bott and L. Tu, Differential Forms in Algebraic Topology, Springer, 1982.
  12. R. Miranda, Algebraic curves and Riemann surfaces, Graduate Studies in Math., AMS, 1995.


Grades will be based on homework, projects, and exams.