5
$\begingroup$

For the past few weeks I have been starting to learn about complex geometry and Hodge theory. I'm doing so with the book of Daniel Huybrechts Complex Geometry, which is an excellent book, however I would like to supplement this book with some online lectures.

Is there anyone who can recommend me a lecture series which I can use to learn about complex geometry and related topics?

$\endgroup$

1 Answer 1

9
$\begingroup$

Books

1.You can refer to Complex Manifolds written by James Morrow and Kunihiko Kodaira.

It is an excellent primer including a lot of calculations and details.

2.You can refer to Principal of Algebraic Geometry written by Griffiths and Harris and Complex Analytic and Differential Geometry written by Jean-Pierre Demailly.

They have more differential-geometric points of view.

3.You can refer to Hodge Theory and Complex Algebraic Geometry 1 written by Claire Voisin.

It may be more difficult and advanced and have more algebraic points of view.


Notes and Lectures

1.Notes about complex manifolds which is a wonderful supplement of the Huybrechts' book.

:https://www.math.stonybrook.edu/~cschnell/pdf/notes/complex-manifolds.pdf

2.New lectures written by Hossein Movasati about the Hodge theory.

:http://w3.impa.br/~hossein/myarticles/hodgetheory.pdf

3.If you interested in Kahler Manifolds,you can see the lectures written by Werner Ballmann.

:http://people.mpim-bonn.mpg.de/hwbllmnn/archiv/kaehler0609.pdf


Videos

1.Hans-Joachim Hein's Complex Geometry that consisting of ten classes is nice. See here :https://m.youtube.com/results?search_query=complex+geometry

2.Complex Analytic and Algebraic Geometry by Qaisar Latif.

See here: https://m.youtube.com/playlist?list=PLWy-AYZriyMGZjZQ7I8kYhZhtlUzFcWcz

$\endgroup$
4
  • $\begingroup$ Thank you very much, however I would also be very interested in online video lectures. Do you know any? $\endgroup$ Oct 12, 2019 at 9:47
  • $\begingroup$ I added it in my answer. Hope you have a wonderful trip in complex geometry! $\endgroup$
    – Invariance
    Oct 12, 2019 at 13:21
  • $\begingroup$ ad Videos, 1. Is the course by Hein still available? Can't find it. $\endgroup$
    – Mathy
    Nov 17, 2020 at 9:09
  • $\begingroup$ Dear @Mathy, I also cannot find it, anyway there're still several nice resources online. $\endgroup$
    – Invariance
    Nov 22, 2020 at 6:59

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .