Analytic and Algebraic Geometry

Research topics

The main research areas are in the field of Algebraic Geometry, and there are some researches in the area of Complex Analysis.
We summarize their topics in the following:

• Classification problems for projective varieties. This consider the three main classes of projective varieties, namely curves, surfaces and higher dimensional varieties. In the last case special emphasize is on the so called Mori theory (or Minimal Model Program) with important results for the case of dimension 4 and 5. In the case of surfaces the main object of study is the moduli spaces of minimal surfaces of general type.
• Special algebraic varieties (e.g. Fano manifolds, Moishezon manifolds, almost homogeneous manifolds).
• Vector bundles and related problems.
• Real algebraic geometry: Nash functions and compact algebraic varieties.
• Topology of normal surface singularities (by means of generic covers of the plane).
• Differential topology of low dimensional manifolds.
• Computational tools which are often used in the study of the above problems.
• Several complex variables and complex analytic geometry, hypercomplex analysis: CR functions and pluriharmonic functions, regular quaternionic functions and Clifford Analysis.

See also the Multimedia Geometry Group

Staff