Periods of hypersurfaces --- CAG L26.1

We state the Torelli theorem for hypersurfaces. We then explain how the period matrix expresses the Hodge decomposition on the cohomology of a hypersurface. Along the way, we introduce the Hodge filtration which is more natural than the Hodge decomposition and we introduce primitive cohomology.

0:00 Periods and Hodge decomposition
2:40 Torelli theorem for hypersurfaces
5:04 Exceptions
8:07 Goal and next steps
9:20 Hodge filtration
12:47 Primitive cohomology
15:41 Period matrix
21:41 Very general hypersurface
23:02 Coming up next...

== Relevant resources ==

Website for this lecture:

Torelli theorem for hypersurfaces:
Donagi -- "Generic torelli for projective hypersurfaces"
Voisin -- Schiffer variations and the generic Torelli theorem for hypersurfaces

Torelli theorem for the Quintic threefold:
A generic Torelli theorem for the quintic

== General description ==

This video is part of my "Computational Algebraic Geometry" lecture series taking place in Leibniz University Hannover (Germany).

Videos will be uploaded weekly on Monday and Wednesday afternoons during lecture times of the Winter Semester 2021/2022.