FOR 790:  Classification of Algebraic Surfaces and Compact Complex Manifolds

• Subject Area: Mathematics
• Term: from 2007 to 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 27316708

The Research Unit focuses on problems in the theory of complex and real algebraic surfaces and, more generally, in complex geometry. A common feature of all our projects is "classification theory": of complex respectively real surfaces and of complex varieties in general. On one hand, classification means producing concrete lists of varieties together with a description of their special geometry and of other characteristic features. The search for mutual dependence of numerical invariants and geometric properties also comes under this heading. But classification also includes deformation theoretical aspects and the study of moduli spaces.
Key tools are structure results in birational and biholomorphic geometry. Methodologically, many fields of mathematics come into play: complex analysis, algebraic geometry, topology, homological and commutative algebra, group theory and differential geometry.
Because of the broad spectrum of methods applied, this Research Unit provides the opportunity to concentrate the research activities of scientists with different expertise to well defined, sharply focused projects. Moreover, in our proposal the projects are not separated but fairly interwoven, and all participating scientists are involved in more than one project. The variety of aspects of the Research Unit becomes obvious from the list of project titles:
(1) Cones of Kähler and projective manifolds;
(2) Special varieties: geometry and global deformations;
(3) Approximation of Kähler manifolds;
(4) Entire curves and hyperbolicity;
(5) Deformation classes of real and complex manifolds;
(6) Rigid varieties, triangle groups, the action of the absolute Galois group;
(7) Classification and geometry of surfaces of general type.
All research fields are internationally very active and important developments took place in the last years. Preexisting international collaboration can be intensified and put to use throughout the Research Unit.

• DFG Programme: Research Units

Projects

• Approximation of Kähler manifolds (Applicant Peternell, Thomas )
• Classification and geometry of surfaces of general type (Applicants Bauer, Ingrid ;  Catanese, Fabrizio ;  Schröer, Stefan )
• Classification and geometry of surfaces of general type (Applicants Bauer, Ingrid ;  Catanese, Fabrizio )
• Cones of Kähler and projective manifolds (Applicant Kebekus, Stefan )
• Deformation classes of real and complex manifolds (Applicant Catanese, Fabrizio )
• Differential forms on singular spaces and classification theory (Applicant Kebekus, Stefan )
• Entire Curves and Hyperbolicity (Applicant Winkelmann, Jörg )
• Global deformations and symmetries (Applicant Peternell, Thomas )
• Koordinatorfonds (Applicant Catanese, Fabrizio )
• Koordinatorfonds (Applicant Catanese, Fabrizio )
• Rational Points on Surfaces of General Type (Applicant Stoll, Michael )
• Rigid varieties, triangle groups, the action of the absolute Galois group (Applicant Singhof, Wilhelm )
• Special varieties: geometry and global deformations (Applicants Peternell, Thomas ;  Schröer, Stefan )
• Stability of vector bundles and rational quotients (Applicants Kebekus, Stefan ;  Peternell, Thomas )
• Topological invariants of deformation classes of real and complex manifolds (Applicant Catanese, Fabrizio )

• Spokesperson: Professor Dr. Fabrizio Catanese