Spring School: Rational Curves and Contact Geometry

Speakers:

Stéphane Druel (Grenoble)

Thomas Peternell (Bayreuth)

Jarosław Wiśniewski (Warsaw)

This spring school is intended for advanced master students, PhD students and Postdocs in Algebraic Geometry. Its intention is to provide an introduction to the theory of moduli of rational curves and its application to the contact geometry.

Please note that details of the following program might be tentative only:

Stéphane Druel: Geometry of rational curves 

1. The space of rational curves, dimension estimates.
   
2. Existence of rational curves.
   
3. Families of singular rational curves.
   
4. Characterization of the projective space (Cho/Miyaoka/Shepherd-Barron, Kebekus).
   
5. Varieties of minimal rational tangents (birationality of the tangent morphism, singular VMRT).

Thomas Peternell: Fano manifolds and an elementary introduction to Mori theory 

1. The minimal model program in dimension 2.
   
2. Fano manifolds I (definition, basic properties, examples).
   
3. Fano manifolds II (boundedness, classification).
   
4. Vanishing and non-vanishing theorems.
   
5. Minimal model program in higher dimensions.
   

Jarek Wisniewski: Contact Geometry

1. Contact structure on complex manifolds and relation to holonomy.
2. Contact and related symplectic structures. Examples.
3. The bundle of first jets. Spannedness of jets and homogenity.
   
4. Towards the classification of complex contact manifolds.
   
5. VMRT's are Legendrian

Literature

1. Beauville, Riemannian holonomy and algebraic geometry. Enseign. Math. 53 (2007), 97–126; http://arxiv.org/abs/math/9902110
   
2. Beauville, Fano contact manifolds and nilpotent orbits. Comment. Math. Helv. 73 (1998), 566–583. http://arxiv.org/abs/alg-geom/9707015
   
3.  Buczyński, Legendrian subvarieties of projective space. Geom. Dedicata 118 (2006), 87–103. http://arxiv.org/abs/0805.3848
   
4. Demailly, On the Frobenius integrability of certain holomorphic p-forms. in Complex geometry (Göttingen, 2000), 93–98, Springer, Berlin, 2002. http://arxiv.org/abs/math/0004067
   
5. Kebekus, Lines on complex contact manifolds. II. Compos. Math. 141 (2005), 227–252. http://arxiv.org/abs/math/0306260
   
6. Kebekus, Peternell, Sommese, Wiśniewski, Projective contact manifolds. Invent. Math. 142 (2000), 1–15. http://arxiv.org/abs/math/9810102

Schedule:

Registration will be in room 05-432 (5th floor).

Organizers:

Manfred Lehn (Mainz)

Thomas Peternell  (Bayreuth)

Registration and Financial Support

Full financial support is available for members of the SFB/TRR 45. There is limited support (accomodation in one of the two hotels listed below) for other participants, too.  

Registration is possible until March 5, 2014.

Accomodation

We have reserved a block of rooms at Hotel Advena and Cityhotel Neubrunnenhof , both hotels are located close to the main train station in Mainz. Please state the key word "Spring School University of Mainz" when contacting one of the hotels. Please note, however, that the number of rooms is limited and rooms are allocated on a "first come - first serve" basis so early reservation is recommended.

If you prefer to make reservations in another hotel, we refer to the home page of the City of Mainz where you will find a detailed list of hotels in and around Mainz.

Travel information

All lectures will take place at the Institute of Mathematics of the University of Mainz, Staudinger Weg 9, in room 05-426.

The next bus stop when coming from the city centre/main station (e.g. bus lines 9, 54, 55, 58, 68) is "Friedrich-von-Pfeiffer-Weg".

Maps

• Map of Campus
• Location of Campus within the City of Mainz