% Session SMF l'Etat de la Recherche, Grenoble, 25-26-27 Novembre 1994
% Texte pour Panoramas et Synth\`eses
% Plain-TeX
% J. Bertin, J.P. Demailly, Ch. Peters, L. Illusie
% Pages de t\^ete

\input hodge-macros.tex
\font\twentyeightbf=cmbx10 at 28pt
\font\twentybf=cmbx10 at 20pt

\centerline{\twentybf PANORAMAS ET SYNTH\`ESES 3}
\vskip6cm

% Page i
\centerline{\twentyeightbf INTRODUCTION \`A LA}
\bigskip
\centerline{\twentyeightbf TH\'EORIE DE HODGE}
\vskip1.5cm

\centerline{\twentybf Jos\'e Bertin, Jean-Pierre Demailly}
\vskip5mm
\centerline{\twentybf Luc Illusie, Chris Peters}
\vfill

\centerline{\seventeenbf Soci\'et\'e Math\'ematique de France 1996}
\eject

% Page ii
\blankline
\headline={\hfil}\fst=-2
\footline={\hfil AMS Subject classification: 
14C30, 14D07, 14F17, 13A35, 58A14\hfil}
\pagejump


% Page iii
$$
\special{"
3 dup scale
2 currentscreen 4 2 roll mul 3 1 roll setscreen
  -48.250 -17.000 translate
/diamond
{10.000  25.000 moveto  30.000  25.000 lineto  37.000  18.000 lineto
 22.000   5.000 lineto  18.000   5.000 lineto   3.000  18.000 lineto
 closepath stroke 
  3.000  18.000 moveto  37.000  18.000 lineto stroke
 20.000  25.000 moveto  20.000   5.000 lineto stroke
 12.000  25.000 moveto   8.000  18.000 lineto stroke
  8.000  18.000 moveto  19.000   5.000 lineto stroke
 28.000  25.000 moveto  32.000  18.000 lineto stroke
 32.000  18.000 moveto  21.000   5.000 lineto stroke
} def
 46.000  18.000 moveto  80.000  34.000 lineto
114.000  18.000 lineto  80.000   2.000 lineto 
closepath 0.900 setgray fill
  0.000 setgray
 22.000   9.000 translate  
  0.500 dup scale
  0.500 setlinewidth
diamond
192.000   0.000 translate
diamond}
\matrix{
&&&~~1~~&&&\cr
&&~~0~~&&~~0~~&&\cr
&~~0~~&&h^{1,1}&&~~0~~&\cr
~~1~~&&h^{2,1}&&h^{1,2} &&~~1~~\cr
&~~0~~&&h^{1,1}&&~~0~~&\cr
&&~~0~~&&~~0~~&&\cr
&&&~~1~~&&&\cr}
$$
\vskip1.8cm

\centerline{\twentyeightbf INTRODUCTION \`A LA}
\bigskip
\centerline{\twentyeightbf TH\'EORIE DE HODGE}
\vskip1cm

\centerline{\twentybf Jos\'e Bertin, Jean-Pierre Demailly}
\vskip5mm
\centerline{\twentybf Luc Illusie, Chris Peters}
\vskip1cm

Le pr\'esent ouvrage d\'eveloppe un certain nombre d'\'el\'ements
fondamentaux de la th\'eorie de Hodge. Il est destin\'e principalement
aux \'etudiants et chercheurs non sp\'ecialistes du sujet, qui
souhaitent se familiariser en profondeur avec celui-ci et se faire une
id\'ee de l'\'etat actuel de la recherche. Le texte comporte trois
parties consacr\'ees \`a des aspects vari\'es et compl\'ementaires de la
th\'eorie: aspects analytiques (m\'ethodes $L^2$), alg\'ebriques
(utilisation de la caract\'eristique~$p$), et enfin applications \`a
la g\'eom\'etrie alg\'ebrique au travers de l'\'etude des variations de
structure de Hodge et des conjectures de sym\'etrie miroir pour les
vari\'et\'es de Calabi-Yau.
\bigskip

This monograph develops a number of fundamental concepts and results of
Hodge Theory. It is mainly aimed to students and researchers,
non-experts in the field, who wish to get acquainted in depth with the
subject and obtain precise up-to-date information on the current status
of the theory. The manuscript is divided in three parts, each of them
devoted to various and complementary aspects of the theory: analytic
aspects ($L^2$ methods), algebraic aspects (use of characteristic $p$
methods), applications to algebraic geometry through a study of
variations of Hodge structures and mirror symmetry conjectures for
Calabi-Yau manifolds.

\footline{\hfill\copyright\ Panoramas et Synth\`eses 3, SMF 1996}

\end

