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Brief course description:
I will give an introduction to the complex analytic side of algebraic geometry, (very)
roughly modeled after the first two-three
chapters in Griffiths-Harris. 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 then aim for the Kodaira embedding
and vanishing theorem, and the weak and hard Lefschetz theorems, plus some explicit geometry through
examples. We will continue
this material next semester, when I will also discuss Hodge structures, polarizations,
complex Abelian varieties and deformations of complex structures, among other things.
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