Derived Algebraic Geometry Seminar — Fall 2017
Organization
- Organization
- Johan Commelin
and Salvatore Floccari
- Location
- Israëlslaan 118, Kelder 1.02. (Exceptions: see below)
- Time
- 1400–1545, Friday. (Exceptions: see below)
Please note that there is a sibling seminar on Friday mornings:
the Stacks seminar.
Description
The goal of the seminar is to learn the basics of derived algebraic geometry with the purpose of understanding Huybrechts's proof of the following theorem.
Theorem.
Let $S$ and $S'$ be two projective complex K3 surfaces and let $\phi\colon H^2(S,\mathbb{Q}) \to H^2(S',\mathbb{Q})$ be an Hodge isometry between them. Then $\phi$ yields an algebraic class in $H^{2,2}(S\times S',\mathbb{Q})$. In other words, $\phi$ is induced by an algebraic correspondence between $S$ and $S'$.
This result was first proven via analytic methods by Buskin. (Lenny Taelman organised an
Intercity Seminar on his proof in the spring of 2016.)
In contrast, Huybrechts's proof uses the language of derived algebraic geometry and Fourier–Mukai transforms in particular.
During the course of the seminar, we will learn these techniques, and finally we discuss the proof of the aforementioned theorem. Our main reference is Huybrechts's book
Fourier–Mukai transforms in algebraic geometry, and his preprint
Motives of isogenous K3 surfaces.
Schedule and location
A tentative schedule of talks can be found
here.
| Date | Talk |
|---|
Fri, Oct 06
(1100–1245) |
Salvatore Floccari —
Triangulated categories and the derived category of coherent sheaves.
|
Fri, Oct 13
|
Johan Commelin — A theorem of Bondal and Orlov.
[Notes]
|
Fri, Oct 20
|
Salvatore Floccari —
Fourier Mukai tranforms and Orlov's theorem.
|
Fri, Oct 27
|
Salvatore Floccari —
Fourier Mukai tranforms and Orlov's theorem (continued).
Ties Laarakker —
Fourier Mukai tranforms and abelian varieties.
|
Fri, Nov 10
(Duistermaatzaal,
5th floor,
HFG) |
Ties Laarakker —
Fourier Mukai tranforms and abelian varieties (continued).
|
Fri, Nov 24
(Springerzaal,
7th floor,
HFG) |
Johan Commelin —
Twisted sheaves.
[Notes]
|
Fri, Dec 08
(Springerzaal,
7th floor,
HFG) |
Wessel Bindt —
Twisted Fourier-Mukai functors and twisted Chern characters.
|
Literature
The main source is the aforementioned book by Huybrechts,
Fourier–Mukai transforms in algebraic geometry.