Hodge Theory on Algebraic Varieties, M.Sc. Thesis Sharif University of Technology ; Jafari, Amir (Supervisor)
Abstract
Cohomology groups of complex algebraic varieties with coefficients in ℂ, can be considered more than just a vector space and they can equipped with various and rich linear algebra structures which are functorial with respect to morphisms between them. In this thesis we first review classic Hodge theory, Hodge decomposition and Lefschetz decomposition theorems which enable us to introduce the concept of pure Hodge structure on cohomology group H^n (X,C) of a compact Kähler manifold X. Then we define Frölicher spectral sequence for a complex manifold X and show that it will degenerate at E_1 when X is compact and Kähler. For generalization of pure Hodge structures to smooth non...
Cataloging briefHodge Theory on Algebraic Varieties, M.Sc. Thesis Sharif University of Technology ; Jafari, Amir (Supervisor)
Abstract
Cohomology groups of complex algebraic varieties with coefficients in ℂ, can be considered more than just a vector space and they can equipped with various and rich linear algebra structures which are functorial with respect to morphisms between them. In this thesis we first review classic Hodge theory, Hodge decomposition and Lefschetz decomposition theorems which enable us to introduce the concept of pure Hodge structure on cohomology group H^n (X,C) of a compact Kähler manifold X. Then we define Frölicher spectral sequence for a complex manifold X and show that it will degenerate at E_1 when X is compact and Kähler. For generalization of pure Hodge structures to smooth non...
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