Complex Manifolds

I am lecturing Part III Complex Manifolds in Lent Term 2019. The lectures are 12:00 - 13:00 on Tuesdays, Thursdays and Saturdays in MR14.

• Example Sheet 1. The examples classes will be 13:30 - 14:30 and 14:30 - 15:30 on 31st January in MR15.
• Example Sheet 2 (updated 8th February). The examples classes will be 13:30 - 14:30 and 14:30 - 15:30 on 14th February in MR15.
• Example Sheet 3 (updated 21st February). The examples classes will be 13:30 - 14:30 and 14:30 - 15:30 on 28th February in MR13.
• Example Sheet 4 (updated 15th March). The examples classes will 13:30 - 14:30 (MR14) and 14:30 - 15:30 (MR11) on 14th March.

The examples classes will be given by Brunella Torricelli.

The revision class will be 12:00-13:00 in MR14 on Friday 3rd May.

If you have any questions about the course, please email me: rd430(at)cam.ac.uk.

Notes:

The (del-bar) Poincaré Lemma in one variable (with a couple of typos corrected).

The relationship between vector bundles and Čech cocycles. We did the rank one case in lectures, the general case is similar once one defines Čech cohomology appropriately (which is done in this link).

On irreducibility (not) being an open property.

Signs for the Hodge star operator on bundles (now consistent with the manifold case).

Books: Most of the course follows Huybrechts' "Complex Geometry: An Introduction". For sheaf theory and Čech cohomology we cover around the same amount as Griffiths-Harris' "Principles of Algebraic Geometry". A more thorough reference for cohomological aspects is Voisin's "Hodge Theory and Complex Algebraic Geometry I". All are available from the library.