Master Seminar: Geometry of moduli stacks
Termin: Freitag 14-16 Uhr in WSC-S-U-3.01.
Dozenten J. Heinloth.
Due to the special circumstances this seminar will take place online through BigBlueButton – please contact the organizer for information on how to join
In both complex and algebraic geometry it is of fundamental interest to construct and study parameter spaces of geometric objects like vector bundles, (elliptic) curves etc. Those moduli spaces are usually not complex manifolds or algebraic varieties themselves but what one calls a stack (german: Stack, french: champ). We have the following hierarchy:
(analytic/algebraic spaces) ⊂ (analytic/algebraic stacks)
Aim of the seminar is to learn what these are by studying prototypical examples of stacks like
(1) stacky curves
(2) moduli spaces of elliptic curves
(3) moduli spaces of vector bundles.
In order to attend the seminar, you should be familiar with either complex or algebraic geometry as covered by a two semester course. Depending on the background of the participants the seminar will be either more algebraic or more analytic/topoogical. The program discussion takes place in room
WSC-S-3.14 on Tuesday February 11 at 15:00.
In case you are interested but can not join the program discussion, please contact me, e.g. by email.
|Two Examples: Elliptic curves and Vector bundles
|Moduli spaces I: Definition and Examples
|Moduli spaces II: Gluing and Descent
|Stacks: Fibered categories or pseudo functors
|The 2-Yoneda lemma and representable morphisms
|Differentiable/Algebraic stacks: Properties and examples
|Groupoids and Quotients
|Vector bundles on curves I
|Vector bundles on curves II