Home

Abstracts for Topics in Algebraic Geometry: Fano Varieties

Alternatively have a look at the program.

Basic properties of Fano varieties

Posted in
Speaker: 
Ariyan Javanpeykar, Ronan Terpereau
Affiliation: 
Mainz, MPIM Bonn
Date: 
Fri, 06/11/2015 - 14:15 - 17:45
Location: 
MPIM Seminar Room
Parent event: 
Topics in Algebraic Geometry: Fano Varieties

We discuss families of Fano varieties and prove their many basic properties
as in Chapter 2 of [6]. We also discuss some of the vanishing results proven by
Shepherd-Barron in his paper on Fano threefolds [7]. We introduce the three
basic invariants:  (Picard number), i (index) and d (degree). We prove their
basic properties.
Finally, we present some of Mori’s results on Fano varieties over fields of
characteristic zero; see Debarre’s book Chapter 4 (and especially 4.3) [3, Cor.
4.18]. For instance, we prove that Fano varieties over C are (topologically)

Mori fibre spaces, and more on the intermediate Jacobian of X_10

Posted in
Speaker: 
Andrea Fanelli, Giovanni Mongardi
Date: 
Fri, 04/12/2015 - 14:15 - 17:45
Location: 
MPIM Seminar Room
Parent event: 
Topics in Algebraic Geometry: Fano Varieties

In the first talk we briefly recall the definition of a Mori fiber space. Then,
we show that for a Fano variety to be a general fibre of a Mori fibre space is
a rather restrictive condition. More precisely, we will give two criteria (one
sufficient and one necessary) for a Q-factorial Fano variety with terminal singularities
to be realised as a fibre of a Mori fibre space. These criteria give a
characterisation of rigid Fano varieties arising as a general fibre of a Mori fibre
space. We apply our criteria to Fano varieties of dimension at most three and

 

... back to parent event

LaTeX version

© MPI f. Mathematik, Bonn Impressum & Datenschutz
-A A +A