Brief course description:
I will give an introduction to the complex analytic side of geometry, with a
view towards algebraic geometry, (very) roughly modeled after the first twothree
chapters in GriffithsHarris. We will discuss the de Rham theorem, the decomposition
of forms according to type, the Kaehler condition, cohomology of analytic sheaves,
and how all of this leads to Hodge theory. We will aim for the Kodaira embedding
and vanishing theorem, and the weak and hard Lefschetz theorems. We will continue
this material next quarter, when I will also discuss Hodge structures, polarizations,
and complex Abelian varieties among other things.
