{"id":173,"date":"2016-12-19T11:20:39","date_gmt":"2016-12-19T10:20:39","guid":{"rendered":"https:\/\/algant.apps.math.cnrs.fr\/\/?page_id=173"},"modified":"2026-01-29T15:18:42","modified_gmt":"2026-01-29T14:18:42","slug":"geometry-25-26","status":"publish","type":"page","link":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/cours\/geometry-25-26\/","title":{"rendered":"Geometry (2025-26 and 2026-27)"},"content":{"rendered":"\n<p><strong>Introduction to K\u00e4hler Geometry and Hodge theory<\/strong><\/p>\n\n\n<p>Teachers:\u00a0 Vincent Koziarz and Andrea Fanelli<\/p>\n<p><strong>Program:<\/strong><\/p>\n<p>In this course, we will deal with higher dimensional complex geometry, with a focus on K\u00e4hler manifolds. This course is complementary to the course of algebraic geometry, but we will give a preference to transcendental methods.<\/p>\n<p>The following topics will be discussed<\/p>\n<ul>\n<li>Introduction to holomorphic functions of several variables<\/li>\n<li>Complex manifolds, de Rham and Dolbeault cohomology<\/li>\n<li>Sheaves and cohomology<\/li>\n<li>Vector bundles, connections and curvature<\/li>\n<li>Harmonic theory on compact complex manifolds, Hodge theory<\/li>\n<li>K\u00e4hler manifolds, Hodge decomposition<\/li>\n<li>Line bundles, first Chern class, notions of positivity for the curvature, Kodaira vanishing theorem<\/li>\n<li>Kodaira embedding theorem<\/li>\n<\/ul>\n<p>Bibliography:<\/p>\n<p>J.-P. Demailly: <em>Complex analytic and algebraic geometry, available on the web page of J.-P. Demailly.<\/em><br \/>\nP. Griffiths et J. Harris: <em>Principles of algebraic geometry, Wiley &amp; Sons, 1978<\/em><br \/>\nS. Kobayashi: <em>Differential geometry of complex vector bundles, Princeton University Press, 1987<\/em><br \/>\nR.O. Wells: <em>Differential analysis on complex manifolds, GTM 65, Springer, 1980<\/em><\/p>","protected":false},"excerpt":{"rendered":"<p>Introduction to K\u00e4hler Geometry and Hodge theory Teachers:\u00a0 Vincent Koziarz and Andrea Fanelli Program: In this course, we will deal with higher dimensional complex geometry, with a focus on K\u00e4hler manifolds. This course is complementary to the course of algebraic geometry, but we will give a preference to transcendental methods. The following topics will be &hellip; <a href=\"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/cours\/geometry-25-26\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Geometry (2025-26 and 2026-27)&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":4,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-173","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/pages\/173","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/comments?post=173"}],"version-history":[{"count":8,"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/pages\/173\/revisions"}],"predecessor-version":[{"id":638,"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/pages\/173\/revisions\/638"}],"up":[{"embeddable":true,"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/pages\/4"}],"wp:attachment":[{"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/media?parent=173"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}