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\begin{document}

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\section*{Hodge theory and Complex algebraic geometry}

This page collects material related to the textbook

\begin{itemize}%
\item [[Claire Voisin]],

\emph{Hodge theory and Complex algebraic geometry I,II},

Cambridge Stud. in Adv. Math. \textbf{76, 77}, 2002/3



\end{itemize}
on [[Hodge theory]] and [[GAGA]].

\hypertarget{contents}{}\section*{{Contents}}\label{contents}

\noindent\hyperlink{volume_1}{Volume 1}\dotfill \pageref*{volume_1} \linebreak
\noindent\hyperlink{i_preliminaries}{I Preliminaries}\dotfill \pageref*{i_preliminaries} \linebreak
\noindent\hyperlink{1_holomorphic_functions_of_many_variables}{1 Holomorphic functions of many variables}\dotfill \pageref*{1_holomorphic_functions_of_many_variables} \linebreak
\noindent\hyperlink{2_complex_manifold}{2. Complex manifold}\dotfill \pageref*{2_complex_manifold} \linebreak
\noindent\hyperlink{3_khler_metric}{3. K\"a{}hler metric}\dotfill \pageref*{3_khler_metric} \linebreak
\noindent\hyperlink{4_sheaves_and_cohomology}{4. Sheaves and cohomology}\dotfill \pageref*{4_sheaves_and_cohomology} \linebreak
\noindent\hyperlink{ii_the_hodge_decomposition}{II The Hodge decomposition}\dotfill \pageref*{ii_the_hodge_decomposition} \linebreak
\noindent\hyperlink{5_harmonic_forms_and_cohomology}{5. Harmonic forms and cohomology}\dotfill \pageref*{5_harmonic_forms_and_cohomology} \linebreak
\noindent\hyperlink{6_the_case_of_khler_manifolds}{6. The case of K\"a{}hler manifolds}\dotfill \pageref*{6_the_case_of_khler_manifolds} \linebreak
\noindent\hyperlink{7_hodge_structures_and_polarization}{7. Hodge structures and polarization}\dotfill \pageref*{7_hodge_structures_and_polarization} \linebreak
\noindent\hyperlink{8_holomorphic_de_rham_complexes_and_spectral_sequences}{8. Holomorphic de Rham complexes and spectral sequences}\dotfill \pageref*{8_holomorphic_de_rham_complexes_and_spectral_sequences} \linebreak
\noindent\hyperlink{iii_variations_of_hodge_structures}{III Variations of Hodge structures}\dotfill \pageref*{iii_variations_of_hodge_structures} \linebreak
\noindent\hyperlink{9_families_and_deformations}{9. Families and deformations}\dotfill \pageref*{9_families_and_deformations} \linebreak
\noindent\hyperlink{10_variations_of_hodge_structure}{10. Variations of Hodge structure}\dotfill \pageref*{10_variations_of_hodge_structure} \linebreak
\noindent\hyperlink{iv_cycles_and_cycle_classes}{IV. Cycles and cycle classes}\dotfill \pageref*{iv_cycles_and_cycle_classes} \linebreak
\noindent\hyperlink{11_hodge_classes}{11. Hodge classes}\dotfill \pageref*{11_hodge_classes} \linebreak
\noindent\hyperlink{12_delignebeilinson_cohomology_and_the_abeljacobi_map}{12. Deligne-Beilinson cohomology and the Abel-Jacobi map}\dotfill \pageref*{12_delignebeilinson_cohomology_and_the_abeljacobi_map} \linebreak
\noindent\hyperlink{volume_2}{Volume 2}\dotfill \pageref*{volume_2} \linebreak


\hypertarget{volume_1}{}\subsection*{{Volume 1}}\label{volume_1}

\hypertarget{i_preliminaries}{}\subsubsection*{{I Preliminaries}}\label{i_preliminaries}

\hypertarget{1_holomorphic_functions_of_many_variables}{}\paragraph*{{1 Holomorphic functions of many variables}}\label{1_holomorphic_functions_of_many_variables}

\begin{itemize}%
\item [[holomorphic function]]

\end{itemize}
\hypertarget{2_complex_manifold}{}\paragraph*{{2. Complex manifold}}\label{2_complex_manifold}

\begin{itemize}%
\item [[complex manifold]]


\item [[Newlander-Nirenberg theorem]]


\item [[Dolbeault complex]]



\end{itemize}
\hypertarget{3_khler_metric}{}\paragraph*{{3. K\"a{}hler metric}}\label{3_khler_metric}

\begin{itemize}%
\item [[Kähler manifold]]

\end{itemize}
\hypertarget{4_sheaves_and_cohomology}{}\paragraph*{{4. Sheaves and cohomology}}\label{4_sheaves_and_cohomology}

\begin{itemize}%
\item [[abelian sheaf cohomology]]

\end{itemize}
\hypertarget{ii_the_hodge_decomposition}{}\subsubsection*{{II The Hodge decomposition}}\label{ii_the_hodge_decomposition}

\hypertarget{5_harmonic_forms_and_cohomology}{}\paragraph*{{5. Harmonic forms and cohomology}}\label{5_harmonic_forms_and_cohomology}

\begin{itemize}%
\item [[harmonic differential form]]


\item [[Hodge theorem]]



\end{itemize}
\hypertarget{6_the_case_of_khler_manifolds}{}\paragraph*{{6. The case of K\"a{}hler manifolds}}\label{6_the_case_of_khler_manifolds}

\begin{itemize}%
\item [[hard Lefschetz theorem]]


\item [[Lefschetz decomposition]]



\end{itemize}
\hypertarget{7_hodge_structures_and_polarization}{}\paragraph*{{7. Hodge structures and polarization}}\label{7_hodge_structures_and_polarization}

\begin{itemize}%
\item [[Hodge structure]]


\item [[polarized variety]]



\end{itemize}
\hypertarget{8_holomorphic_de_rham_complexes_and_spectral_sequences}{}\paragraph*{{8. Holomorphic de Rham complexes and spectral sequences}}\label{8_holomorphic_de_rham_complexes_and_spectral_sequences}

\begin{itemize}%
\item [[hypercohomology]]


\item [[holomorphic de Rham complex]]


\item [[differential form with logarithmic singularities]]


\item [[spectral sequence]]


\item [[Frölicher spectral sequence]]



\end{itemize}
\hypertarget{iii_variations_of_hodge_structures}{}\subsubsection*{{III Variations of Hodge structures}}\label{iii_variations_of_hodge_structures}

\hypertarget{9_families_and_deformations}{}\paragraph*{{9. Families and deformations}}\label{9_families_and_deformations}

\hypertarget{10_variations_of_hodge_structure}{}\paragraph*{{10. Variations of Hodge structure}}\label{10_variations_of_hodge_structure}

\begin{itemize}%
\item [[variations of Hodge structure]]

\end{itemize}
\hypertarget{iv_cycles_and_cycle_classes}{}\subsubsection*{{IV. Cycles and cycle classes}}\label{iv_cycles_and_cycle_classes}

\hypertarget{11_hodge_classes}{}\paragraph*{{11. Hodge classes}}\label{11_hodge_classes}

\hypertarget{12_delignebeilinson_cohomology_and_the_abeljacobi_map}{}\paragraph*{{12. Deligne-Beilinson cohomology and the Abel-Jacobi map}}\label{12_delignebeilinson_cohomology_and_the_abeljacobi_map}

\begin{itemize}%
\item [[Abel-Jacobi map]]


\item [[Deligne cohomology]]



\end{itemize}
\hypertarget{volume_2}{}\subsection*{{Volume 2}}\label{volume_2}

(\ldots{})

category: reference



\end{document}