Spring school on Algebraic Geometry 2011: Invariants and Moduli

Date

The school starts Mo, 14/03/2011 and lasts until Fr, 18/03/2011. The first talk on Monday is at 9 am. Registration is possible from 8:30 until 9 am on Monday. See below for details.

Location

The school will be held at the Institute for Mathematics of the University of Augsburg, 86159 Augsburg, Germany. A map showing how to get to the university is located on the website of the university itself. The lectures are held in room 1005 of building L1 in the institute.

Topics and aim of the school

We organise a one-week school on invariants and moduli in the algebraic and complex geometry setting following the book "An Introduction to Invariants and Moduli" by Shigeru Mukai. Participants should have a good working knowledge on the subject at the end of the week.
The program of the lectures is determined by the organisers.

Organizers

• Samuel Boissière (Université de Nice, France)
• Marco Hien (Universität Augsburg, Germany)
• Marc Nieper-Wißkirchen (Universität Augsburg, Germany)
• Alessandra Sarti (Université de Poitiers, France)

Speakers/Participants

In principal, the school is open to everyone working on an advanced graduate or postgraduate level in algebraic geometry. If possible, each of the participants should give a one-hour lecture on the subject of the school.

Application

Please apply by filling in the application form until 04/02/2011. As every participant is supposed to give a talk (from a list of 23 talks, see below), please state your preferred talks in the application form. Please note that some of the talks are already taken (see below).

Registration

There will be a registration fee of 20 €. Please register yourself on Monday, 14/03/2011, 8:30 am, in room 2006 in building L1.

Accomodation

B&B Hotel Augsburg, Haunstetter Straße 68, 86161 Augsburg.

Financial support

There is limited financial support for boarding expenses and to cover the registration fee.

Schedule

There will be about five lectures of one hour each day. Between them, there should be ample time for discussions.

Day 1 (Monday) - Introduction and Algebraic Groups

Talk 1: Invariants of groups (Robert Gelb, University Augsburg)

Chapter 1.2 of [Mukai]

Talk 2: Classical binary invariants (Anne Grünzig, University Augsburg)

Chapter 1.3

Talk 3: Plane Curves (Jesus Tapia Amador, University of Glasgow)

Chapter 1.4

Talk 4: Period parallelograms and cubic curves (Ayberk Zeytin, Middle East Technical University, Ankara)

Chapter 1.5

Talk 5: Algebraic Groups (Hendrik Verhoek, University of Rome "Tor Vergata")

Chapters 3.3, 4.1, 4.2

Day 2 (Tuesday) - Affine and projective quotients

Talk 1: Hilbert's theorem (Sebastian Krug, University of Hanover)

Chapters 4.3, 4.5 of [Mukai]

Talk 2: The Cayley–Sylvester counting theorem (Sergei Kovalenko, Ruhr-Universität Bochum)

Chapter 4.4

Talk 3: Affine quotients (Constantin Wittenmeier, University Augsburg)

Chapter 5.1

Talk 4:  Classical invariants and the moduli of smooth hypersurfaces in \(\mathbf P^n\) (Luca Benzo, University of Rome "Tor Vergata")

Chapter 5.2

Talk 5: Linearisation and Proj quotients (Malte Wandel, University of Hanover)

Chapter 6.1, 6.2

Day 3 (Wednesday) - The numerical criterion and some applications

Talk 1: Toric varieties and moving quotients (Malek Joumaah, University of Hanover)

Chapter 3.4, 6.3 of [Mukai]

Talk 2: The numerical criterion (Daniel Wortmann, University of Paderborn)

Chapter 7.1

Talk 3: Examples and applications (Maria Donten-Bury, University Warsaw)

Chapter 7.2

Day 4 (Thursday) - Graßmannians and vector bundles

Talk 1: Graßmannians as quotient varieties (Karl Leicht, Université Lille)

Chapter 8.1 of [Mukai]

Talk 2: The Picard group (Frithjof Schulze, University of Hanover)

Chapter 8.4

Talk 3: Vector bundles (Stefanie Anschlag, University of Bonn)

Chapter 8.5

Talk 4: Riemann's inequality for an algebraic curve (Udo Muttray, Johannes Gutenberg University Mainz)

Chapter 9.1

Talk 5: Cohomology spaces, duality, and the genus (Marc Oberschelp, University of Paderborn)

Chapter 9.2, 9.5

Day 5 (Friday) - The Picard variety

Talk 1: Nonsingularity of quotient spaces (Yaroslav Yatsyshyn, University of Paderborn)

Chapter 9.3 of [Mukai]

Talk 2: An algebraic variety with the Picard group as its set of points (Chiara Camere, University of Nice)

Chapter 9.4

Talk 3: The Jacobian as a complex manifold (Markus Klenke, University of Paderborn)

Chapter 9.5

Talk 4: The Picard functor (Daniel Skodlerack, University of Münster)

Chapter 11.1

Talk 5: Examples (Oleksandr Iena, Intl. School for Advanced Studies Trieste)

Chapter 11.3

Literature

1. S. Mukai: Introduction to Invariants and Moduli