Math 555: Complex Mainfolds II

Spring Semester, 2006

Instructor: Anatoly Libgober
Office: SEO 413
Phone: 312-413-2138
Office Hours: MW 11 a.m. or by appointment.

Texts:

1.Hodge Theory and Complex Algebraic Geometry by C.Voisin, Cambridge University Press 2002.
2.C.Simpson, Higgs bundles and local systems. Publ.IHES 1992.
3. C.Simpson, Subspaces of moduli spaces of rank one local systems.Ann.Sc. Ecole Normal Sup. 1993.
4. C.Voisin, On the homotopy type of compact kahler and complex projective manifolds. Inventiones Math. to appear

Hours: The course meets MWF at 1 p.m. in TH 321.

Topics

This course is the second part of the course on Complex manifolds and complex algebraic geometry. It will cover the end of the Part II and Part III (Variation of Hodge structures) of Voisin's book, Riemann-Roch theorem, and Simpson's theory of local systems on projective manifolds (non abelian Hodge theory) and also rank one local systems on quasiprojectve manifolds. I will also discuss recent work of C.Voisin on homotopy types of Kahler and projective manifolds.

Grading and Homework

Grades will be based on midterms and homework problems assigned at regular intervals. Problems will be assigned during classes.

Other Sources

P. Griffiths, J.Harris, Principles of Algebraic Geomerty, Wiley, NY (1978)
J.P.Demailly, Complex Algebraic and Analytic Geometry. download here
A.Libgober, Lectures on the topology of the complements Proc. Lumini Conf. on Singularities 2005.