The focus of this course is the geometrical and topological method to complex manifolds.
We will begin with the basic property of multivariable analytic functions; after that, we will introduce the notion of complex manifolds, examples of complex manifolds, their blow-ups, line bundles and vector bundles over them.
We will then introduce the notion of Kahler manifolds, show that the de Rham cohomology groups of Kahler manifolds come with Hodge decomposition. The application of cohomology to geometry of Kahler manifolds will be discussed.
In the last part of the quarter, we will introduce the notion of connections, curvatures and Chern classes of vector bundles. The implication of positive line bundle will be proved at the end.
This course will be useful for anyone who is interested in topology, differential geometry and algebraic geometry.
Meeting Time: TuTh, 9:30-10:45AM,
And Location: Main Quad 380-381T
Text Book: Complex Geometry, by Daniel Huybrechts
Office Hours: by appointment
Office: 380-383Y,
And Office Phone: 723-4508
E-mail: jli "at" math.stanford.edu
Hodge theory of complex algebraic varieties, C. Voisin
Period mappings and period domains, J. Carlson
Course Works
TBA