Dolbeault cohomology - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T07:08:54Z http://mathoverflow.net/feeds/question/5068 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/5068/dolbeault-cohomology Dolbeault cohomology Learner 2009-11-11T16:48:44Z 2009-11-11T23:11:52Z <p>Hello</p> <p>I am trying to get a good book that explains the Dolbeault Cohomology, does anyone know of a good one?</p> http://mathoverflow.net/questions/5068/dolbeault-cohomology/5070#5070 Answer by Thomas Riepe for Dolbeault cohomology Thomas Riepe 2009-11-11T17:09:23Z 2009-11-11T17:09:23Z <p>The references given in the <a href="http://en.wikipedia.org/wiki/Dolbeault_cohomology" rel="nofollow" title="wikipedia thereon">wikipedia article</a> . </p> http://mathoverflow.net/questions/5068/dolbeault-cohomology/5072#5072 Answer by Danny Calegari for Dolbeault cohomology Danny Calegari 2009-11-11T17:11:59Z 2009-11-11T17:11:59Z <p>Chern's book "Complex manifolds without potential theory" is a good book, and it does explain Dolbeault Cohomology. But it's a short book, and it explains it concisely. If you need more details, you could also try Griffiths-Harris (but I greatly prefer Chern's book).</p> <p>Kodaira's book "Complex manifolds and deformations of complex structures" is much more leisurely, and with great attention paid to exposition and detail (it doesn't appeal to some people, but I enjoyed it a lot).</p> http://mathoverflow.net/questions/5068/dolbeault-cohomology/5075#5075 Answer by David Speyer for Dolbeault cohomology David Speyer 2009-11-11T17:18:37Z 2009-11-11T17:18:37Z <p>I like "Hodge Theory and Complex Algebraic Geometry" by Voisin. The focus is on the Kahler case, but the early explanations of Dolbeaut cohomology are for all complex manifolds.</p> http://mathoverflow.net/questions/5068/dolbeault-cohomology/5078#5078 Answer by S1 for Dolbeault cohomology S1 2009-11-11T17:38:41Z 2009-11-11T17:38:41Z <p>If I remember right there should be something in "Differential Analysis on Complex Manifolds" by Wells.</p> http://mathoverflow.net/questions/5068/dolbeault-cohomology/5083#5083 Answer by David Lehavi for Dolbeault cohomology David Lehavi 2009-11-11T18:08:00Z 2009-11-11T18:08:00Z <p>Chapter 0.2 of Griffith and Harris</p> http://mathoverflow.net/questions/5068/dolbeault-cohomology/5110#5110 Answer by Kevin Lin for Dolbeault cohomology Kevin Lin 2009-11-11T21:53:25Z 2009-11-11T21:53:25Z <p>Another book that covers Dolbeault cohomology very nicely is "Complex Geometry" by Daniel Huybrechts. I highly recommend it.</p>