These are the notes of an introductory course on hodge theory. Adhonorem clairevoisin american mathematical society. Hodge theory and complex algebraic geometry ii like4book. Preliminary notes by kiran kedlaya on delignes lectures, in pdf. Voisin hodge theory and complex algebraic geometry i. Algebraic cycles and hodge theory, lecture notes in mathematics 1594, springer verlag 1994 cime lectures, containing article by voisin. Hodge theory and complex algebraic geometry 1 claire. Volume 1 cambridge studies in advanced mathematics book 76 kindle edition by voisin, claire, schneps, leila. Algebraic cycles and hodge theory lectures given at the. Indeed our presentation usually follows closely one of these texts. Course descriptions and notes university of arizona. The book starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter being treated in a more. You can check out the lecture notes referenced in this mo question hodge theory voisin.
The goal of the course is to give an introduction to the basic results in hodge theory. Cambridge core geometry and topology hodge theory and complex algebraic geometry ii by claire voisin skip to main content accessibility help we use cookies to distinguish you from other users and to provide you with a better experience on our websites. This introductory text to hodge theory and kahlerian geometry is an excellent and modern introduction to the subject, shining with comprehensiveness, strictness, clarity, rigor, thematic steadfastness of purpose, and. Proofs of the lefschetz theorem on hyperplane sections, the picardlefschetz study of lefschetz pencils, and deligne theorems on the degeneration of the leray spectral sequence and the global invariant cycles follow. Hodge theory and complex algebraic geometry i, ii, by claire voisin. Hodge theory and complex algebraic geometry ii by claire. The dominant theme of her work is hodge theory, in particular, its application to concrete classical prob lems. Introduction to hodge theory 3 the decomposition 1. We aim to present materials which are not covered in j. Claire voisin wikipedia bahasa indonesia, ensiklopedia bebas. Hodge theory and complex algebraic geometry i by jayna. Claire voisin is the author of hodge theory and complex algebraic geometry i 4.
An international school on hodge theory took place at the cirm in trento, italy, from 31 august to 4 september 2009. Claire voisin is a french mathematician known for her work in algebraic geometry. Cambridge core geometry and topology hodge theory and complex algebraic geometry ii by claire voisin. The dominant theme of her work is hodge theory, in particular, its application to concrete classical prob. The author then proves the kaehler identities, which leads to the hard lefschetz. Voisins books hodge theory and complex algebraic geometry, i, ii, therefore, the reader will not. Lewiss book a survey of the hodge conjecture and c. Volume 1 cambridge studies in advanced mathematics 9780521718011. Claire voisin born 4 march 1962 is a french mathematician known for her work in algebraic geometry. In fact, hodge theory provides two sets of data on the cohomology of a. Hodge structures on cohomology algebras and geometry. Volume 1 cambridge studies in advanced mathematics by claire voisin this is a modern introduction to kaehlerian geometry and hodge structure. Hodge theory and complex algebraic geometry ii by claire voisin. Use features like bookmarks, note taking and highlighting while reading hodge theory and complex algebraic geometry i.
The key observation is that, given a riemannian metric on m, every cohomology class has a canonical representative, a differential form which vanishes under the laplacian operator of the metric. Downtoearth expositions of hodge theory mathoverflow. Hodge theory and complex algebraic geometry claire voisin. Hodge theory and the topology of compact kahler and complex.
The book starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter being treated in a more theoretical way than is usual in geometry. Entdecken sie hodge theory and complex algebraic geometry i. Cambridge studies in advanced mathematics includes bibliographical references and index. Introduction to hodge theory by daniel matei there is also the following lecture notes by claire voisin herself. Cambridge core algebra hodge theory and complex algebraic geometry i by claire voisin. American mathematical society, providence, ri, 1999. Claire voisin contents 0 introduction 2 1 hodge structures 3.
Hodge theory, like algebraic geometry as a whole, is rich in having many levels of. Volume 1 by claire voisin available from rakuten kobo. B induces a bilinear form on pv, also denoted by b determined by its value on. I would like to thank my fellow lecturers, jacob murre and claire voisin, for. Read hodge theory and complex algebraic geometry i. For a long time, the only known proof of this statement, even in. In mathematics, the hodge conjecture is a major unsolved problem in algebraic geometry that relates the algebraic topology of a nonsingular complex algebraic variety to its subvarieties. Jeanpierre demailly dem96, claire voisin voi02 and raymond wells wel80. Hodge decomposition for double planes the hodge decomposition on the cohomology of double planes. The lectures will be devoted to the study of deformations of pairs consisting of a smooth complex projective variety x and a subscheme z of x, say smooth or lci. Cambridge core algebra hodge theory and complex algebraic geometry i by claire voisin skip to main content accessibility help we use cookies to distinguish you from other users and to provide you with a better experience on our websites. Deformation of pairs and noetherlefschetz type loci abstract. After a phd thesis under arnaud beauvilleatorsay,sheenteredcnrs,whereshe stayeduntil2016,whenshebecameprofessor attheprestigiouscollegedefrance. The 2003 second volume of this account of kaehlerian geometry and hodge theory starts with the topology of families of algebraic varieties.
Download it once and read it on your kindle device, pc, phones or tablets. Master lectures hyperkaehler manifolds, hodge theory. Hodge theory of reducible surfaces hodge decomposition and periods of reducible surfaces. This is a modern introduction to kaehlerian geometry and hodge structure. Hodge, is a method for studying the cohomology groups of a smooth manifold m using partial differential equations.
Volume 1 cambridge studies in advanced mathematics by claire voisin hodge theory and complex algebraic geometry i. She is noted for her work in algebraic geometry particularly as it pertains to variations of hodge structures and mirror symmetry, and has written several books on hodge. The main goal of the cime summer school on algebraic cycles and hodge theory has been to gather the most active mathematicians in this area to. The main consequence of hodge theory can be stated as follows. A final version may eventually appear on kedlayas site. Coverage begins with variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory with the latter being treated in a more theoretical way than is usual in geometry. Variations of hodge structure on calabi yau threefolds. As a first consequence, a geometric theorem of voisin implies that the third unramified cohomology group with q z coefficients vanishes on all uniruled threefolds.
Bertin, demailly, luc illusie, chris peters, introduction to hodge theory ams 1996 claire voisin, hodge theory and the topology of complex kahler and complex projective manifolds survey, pdf claire voisin, hodge theory and complex algebraic geometry i,ii, cambridge stud. Hodge theory and complex algebraic geometry claire. Building upon the blochkato conjecture in milnor ktheory, we relate the third unramified cohomology group with q z coefficients with a group which measures the failure of the integral hodge conjecture in degree 4. Curves in double planes and their cohomology classes. Adhonorem clairevoisin arnaudbeauville,guesteditor. Master lectures hyperkaehler manifolds, hodge theory and chow groups. Hodge theory and complex algebraic geometry i claire voisin. Algebraic cycles and hodge theory lectures given at the 2nd session of the centro internazionale matematico estivo c. So far i have read parts of the relevant parts of griffithsharris and lecture notes on the web, but still dont how understand how to do computations with hodge theory, or for which varieties i. So far, the theory sketched above works for general compact k. The first of two volumes offering a modern introduction to kaehlerian geometry and hodge structure. Search for hodge theory and complex algebraic geometry ii books in the search form now, download or read books for free, just by creating an account to enter our library. More than 1 million books in pdf, epub, mobi, tuebl and audiobook formats.
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