This is the website for the research seminar on Fano varieties.
The seminar will take place at the Max Planck Institute in Bonn and at the University of Mainz on certain Fridays.
Our aim is to treat as many different aspects of Fano varieties such as the classification of Fano threefolds, the boundedness of Fano varieties, the rationality or non-rationality of certain classes of Fano varieties, properties of automorphism groups of Fano varieties, period maps of Fano varieties, Mukai's conjectures on invariants of Fano varieties, and more.
There will be five meetings in total.
14:15h - 15:45h + 16:15h-17:45h, Friday November 6th, Bonn in Seminar room MPI
14:15h - 15:45h + 16:15h-17:45h, Friday November 20th, Mainz in Hillbertraum
14:15h - 15:45h + 16:15h-17:45h, Friday December 4th, Bonn in Seminar Room MPI (NOTE: On Thursday December 3rd there is the SFB meeting at Uni Bonn.)
14:15h - 15:45h + 16:15h-17:45h, Friday January 8th, Mainz in Hilbertraum
January 22nd. Cancelled.
14:00h - 15:00h + 15:30h - 16:30h + 17:00h-18:00h, Tuesday February 2nd, Mainz in Hibertraum (Caution: We start at 14h sharp, and it's on TUESDAY.) (Notes below)
Here is a detailed description of the program:
Every meeting the topic will change, as we hope to touch upon as many different algebro-geometric aspects of Fano varieties. Please find below a brief description of every meeting.
- November 6th: Introduction to Fano varieties and boundedness of the deformation types.
Speakers: Ariyan Javanpeykar & Ronan Terpereau
- November 20th: The non-rationality of the general X_10 via its intermediate Jacobian, and constructing holomorphic symplectic manifolds out of Fano varieties.
Speakers: Enrica Floris & Manfred Lehn
- December 4th: Mori fibre spaces, and more on the intermediate Jacobian of X_10.
Speakers: Andrea Fanelli & Giovanni Mongardi
- January 8th: Fano classification and Differential equations. The Fano threefolds X_14 and cubic threefolds.
Speakers: Duco van Straten & Helge Ruddat
- January 22nd: Cancelled.
- February 2nd: Lifting Fano varieties from characteristic p to characteristic zero, and two talks on Mukai's conjecture for Fano varieties; an inequality involving the pseudo-index, dimension and Picard rank.
Speakers: Axel Stabler & Johannes Hofscheier & Giuliano Gagliardi (There are notes for these talks above)
Some references we will use are:
Olivier Debarre. Fano varieties. In Higher dimensional varieties and rational points (Budapest, 2001), volume 12 of Bolyai Soc. Math. Stud., pages 93–132. Springer, Berlin, 20
R. Shafarevich, editor. Algebraic geometry. V, volume 47 of Encyclopaedia of Mathematical Sciences. Springer-Verlag, Berlin, 1999. Fano varieties, A translation of ıt Algebraic geometry. 5 (Russian), Ross. Akad. Nauk, Vseross. Inst. Nauchn. i Tekhn. Inform., Moscow, Translation edited by A. N. Parshin and I. R. Shafarevich.
I. Shepherd-Barron. Fano threefolds in positive characteristic. Compositio Math., 105(3):237–265, 1997.
For more references see the more detailed description of the program above.
All lectures in Mainz will take place at the Institute of Mathematics of the University of Mainz, Staudinger Weg 9, in the Hilbertraum.
The fastest way to the Institut fur Mathematik Mainz from the Hauptbahnhof (Mainz main railway station) is to take Bus line 69 which departs from platform F. Get off at "Duesbergweg", the Mathematics building is to your right behind the parking lot. (The walk is about 2 minutes.) The timetable for the Bus line 69 ishere .
Alternatively, you may take bus lines 9, 54, 55, 58, 68; the bus stop is "Friedrich-von-Pfeiffer-Weg". From there, walk over the pedestrian bridge to the university campus and follow the street to the right. After about 100 meters there is a left curve. After passing the Mensa (campus cafeteria) you see the Mathematics building right in front of you. (The walk is about 10 minutes.)
All lectures in Bonn will take place at the Max Planck Institut fur Mathematik, Vivatsgasse 7. It is walking distance from the train station; see