Chapter 1 . Topology of Algebraic Varieties , Hodge Decomposition , and Applications
نویسنده
چکیده
In this chapter we will review a number of fundamental facts on the topology of smooth complex projective varieties, and the Hodge decomposition of their singular cohomology with complex coefficients. We will then see them in action by proving the Kodaira Vanishing theorem, the invariance of Hodge numbers under deformations, and the birational invariance of certain Hodge numbers. Some basic references for this material are [GH] Chapter 0 and 1, [La] §3.1 and §4.2, and [Vo].
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