EAGER in Poland

October 2000 - September 2004

The program of EAGER started in October 2000 and was concluded in September 2004. Here we present the summary of EAGER activities related to Polish node of the network.

The tasks of EAGER have been defined as follows:

training of young researchers in Algebraic Geometry through fellowships and mobility;
joint European research projects in Algebraic Geometry;
organisation of summer schools and training courses.

Training of young researchers in Algebraic Geometry through fellowships and mobility

The following people have been awarded EAGER fellowships in Poland:

Pre-docs:
1. Franziska Bittner (Utrecht, Nederlands), 1 month, May 2001.
2. Stavros Papadakis (Athens, Greece), 1 month, September 2001.
3. Daniele Faenzi (Florence, Italy), 1 month, October 2001.
4. Elena Chierici (Trento, Italy), 1 month in March and May 2002.
5. Alexander Kasprzyk (Bath, UK), 1 month, March/April 2003.
6. Christian Meyer (Mainz, Germany), 1 month in Cracow, May 2003.
Post-docs:
1. Jan Wierzba (Germany), 2 months, February 2001 and April 2002.
2. Massimiliano Mella (Ferrara, Italy), 1 month, May 2001.
3. Stavros Papadakis (Athens, Greece), 1 month, November 2001.
4. Luis Edoardo Sola Conde (Spain), 3 months, October and November 2002, August and September 2004.
5. Matthias Franz (Grenoble, France), 1 month in April and August 2003.

Publications related to the researcher's stay in Warsaw:

Franziska Bittner, The universal Euler characteristic for varieties of characteristic zero

C. Ciliberto, M. Mella, F. Russo, Varieties with one apparent double point

Daniele Faenzi, A geometric construction of Tango bundle on P^5

L. E. Sola Conde, J. Wisniewski, On manifolds whose tangent bundle is big and 1-ample

Jan Wierzba, Birational geometry of symplectic 4-folds

J. Wierzba, J. Wisniewski: Small contractions of symplectic 4-folds

The following Polish young researchers visited other nodes of EAGER:

Jan Gorski (Warszawa) visited Nice, EAGER fellowship: 6 months in 2001-2002.
Slawomir Cynk (Krakow) visited Mainz, EAGER fellowship: 6 months in 2001.
Wioletta Syzdek (Krakow) visited Essen and Marburg, EAGER fellowship and DFG: 12 months in 2002-2004.
Adrian Langer (Warszawa) Marie Curie Fellow in Warwick, 24 months in 2000-2002.
Tomasz Szemberg (Krakow) visited Essen, supported by German DFG, 18 months, 2001-2004.
Slawomir Rams (Krakow) visited Erlangen, supported by German DFG, 12 months, 2002.
Oskar Kedzierski (Krakow/Warszawa) visited Marie Curie Training Site in Warwick, 12 months in 2001-2004.
Weronika Buczynska (Warszawa) visited Marie Curie Training Site in Warwick, 9 months in 2003-2004.
Jaroslaw Buczynski (Warszawa) visited Marie Curie Training Site in Warwick, 9 months in 2003-2004.

Courses and schools for young researchers

The following schools have been organized in Poland and partialy supported by EAGER:

24rd Autumn School in Algebraic Geometry: Moduli of vector bundles and group action, Wykno , September 2001, teachers: Giorgio Ottaviani (Firenze, Italy) and Jean Valles (Versailles - Saint Quentin en Yvelines, France), organizers: M. Szurek, J. Wisniewski.
Banach Center School on Linear Series & Syzygies, March 18-22, 2002, Bedlewo (Poland), teachers: Th. Bauer (Marburg), C. Birkenhake (Mainz), T. Szemberg (Krakow); local organizer: T. Szemberg.
Mini school at Banach Center in Warsaw: Characteristic classes of singular varieties, April 22-28, 2002, teachers: Paolo Aluffi (Florida/Bonn) and Joerg Schuermann (Muenster); organizers: P. Pragacz, A. Weber.
Mini school at Banach Center in Warsaw: Stratifications of moduli spaces, May 13-19, 2002, main teacher: Gerard van der Geer (Amsterdam); organizers: P. Pragacz, A. Weber.
25th Autumn School in Algebraic Geometry: Vector bundles over curves and higher dimensional varieties, and their moduli, September 2002, teachers: Peter Newstead (Liverpool) and Adrian Langer (Warszawa); organizers: J. Buczynski, J. Wisniewski.
Mini School at IM PAN: Schubert Varieties, May 2003, Invited speakers: Michel Brion (Grenoble), Anders Skovsted Buch (Aarhus), Richard Rimanyi (Budapest/Ohio), Harry Tamvakis (Waltham/Essen); organizers: P. Pragacz, A. Weber.
26th Autumn School in Algebraic Geometry: "C+ and finite groups actions on affine spaces. Locally nilpotent derivations", September 2003, teachers: Daniel Daigle (Ottawa), Gene Freudenburg (Evansville); organizers: J. Buczynski, M. Koras.
27th Autumn School in Algebraic Geometry: "Algebraic Geometry and Derived Categories", September 2004, teachers: Andrei Caldararu (Philadelphia, US) and Miles Reid (Warwick, UK), organizers: J. Buczynski, J. Wisniewski.

Joint scientific projects

Algebraic group actions and quotients; team: A. A'Campo-Neunen (Konstanz), J-M. Drezet (Paris), J. Hausen (Konstanz), M. Koras (Warsaw), P. Russell (Montreal), J. Swiecicka (Warsaw). Task: notes of 23rd Autumn School in Algebraic Geometry, research/expository articles on current research program in a book published by Hindawi Publishing in 2004, editor: J. Wisniewski (Warsaw). Articles: J-M. Drezet, Luna's slice theorem and applications, A. A'Campo-Neunen, J. Hausen, Toric invariant theory , M. Koras, P. Russell, Linearization problems, J. Swiecicka, Good quotients of reductive group actions - combinatorics in projective spaces
Projective surfaces; team: W. Barth (Erlangen), S. Rams (Krakow). Highlights: construction of surfaces with 3-divisible set of cusps. Publications: W. Barth, S. Rams, On quartics with three-divisible sets of cusps, W. Barth, S. Rams, Projective Surfaces with a three-divisible Set of Cusps
Linear series on algebraic varieties; team: Th. Bauer (Marburg), Ch. Schulze (Marburg), W. Syzdek (Krakow), T. Szemberg (Krakow), S. Rams (Krakow). Publications: T. Szemberg, S. Rams, Simultaneous generation of jets on K3 surfaces , W. Syzdek, Nagata submaximal curves on P^1xP^1; other publications in preparation.
Holomorphic symplectic manifolds; team: J. Wierzba (Berlin), L. Sola Conde (Madrid), J. Wisniewski (Warszawa). Highlights: small symplectic contractions of 4-folds, flops related to resolutions of nilpotent orbits, varieties whose tangent bundle is 1-ample. Preprint: J. Wierzba, J. Wisniewski: Small contractions of symplectic 4-folds , (Duke Math. J.).
Double octic Calabi-Yau manifolds; team: D. van Straten (Mainz), Christian Meyer (Mainz), S. Cynk (Krakow). Highlights: infinitesimal deformations of double coverings, equisingular deformations, Hodge numbers and L-series of certain Calabi-Yau. In preparation: S. Cynk, D. van Straten, Deformations of double coverings of smooth algebraic varities, S. Cynk, C. Meyer, Hodge numbers and L-series of certain Calabi-Yau manifolds
Remmert - Van de Ven problem for complex varieties; team: G-L Occhetta (Trento), L. Sola Conde (Madrid), J. Wisniewski (Warszawa). Highlights: R-VdV problem for toric varieties and products of projective spaces. Publication: GL. Occhetta, J. Wisniewski: On Euler-Jaczewski sequence and Remmert - Van de Ven problem for toric varieties, (2001, Math. Zeit.).
Special higher dimensional varieties; team: M. Andreatta (Trento), J. Wisniewski (Warszawa); highligths: manifolds whose tangent bundle contains an ample locally free subsheaf, quasi-homogeneous 4-folds; publications: M. Andreatta, J. Wisniewski, On manifolds whose tangent bundle contains an ample subbundle, Invent. Math. 146 (2001), M. Andreatta, J. Wisniewski, On quasihomogeneous manifolds-via Brion-Luna-Vust theorem, Bull. U. Mat. Italiana.

Other publications and preprints related to joint activities

M. Andreatta, M. Mella, Morphisms of projective varieties from the viewpoint of minimal model theory, (notes of the 22nd Autumn School in Algebraic Geometry), Dissertationes Mathematicae.
L. Bonavero, F. Campana, J. Wisniewski, Varie'te's projectives complexes dont l'e'clate'e en un point est un Fano, ENS.
Franziska Bittner, The universal Euler characteristic for varieties of characteristic zero.
Daniele Faenzi, A geometric construction of Tango bundle on P^5
Jan Wierzba, Birational geometry of symplectic 4-folds

Financial Report

All entries in the following table are in Polish currency PLN.

Expences\Year 2000/2001 2001/2002 2002/2003 2003/2004

Incoming Young Researchers 26127,76 25682,04 38088,91 8799,88

Networking 20340,68 37356,39 35941,75 18522,40

Overheads 5163,16 7004,27 8225,62 3035,81

Total 51631,60 70042,70 82256,28 28934,53

Polish EAGER Homepage

Expences\Year	2000/2001	2001/2002	2002/2003	2003/2004
Incoming Young Researchers	26127,76	25682,04	38088,91	8799,88
Networking	20340,68	37356,39	35941,75	18522,40
Overheads	5163,16	7004,27	8225,62	3035,81
Total	51631,60	70042,70	82256,28	28934,53