Main Research Interests

Algebraic Geometry:

• BIRATIONAL GEOMETRY, CLASSIFICATION OF ALGEBRAIC VARIETIES AND OF THEIR DEGENERATIONS
  
• CURVES, JACOBIANS AND ABELIAN VARIETIES
  
• CURVES, THEIR FAMILIES AND THEIR MODULI
  
• GEOMETRY OF THE EMBEDDINGS IN PROJECTIVE SPACES
  
• ALGEBRAIC SURFACES AND THEIR MODULI
  
• MODULI SPACES OF VECTOR BUNDLES ON CURVES
  
• MODULI SPACES OF SHEAVES ON K3 SURFACES
  
• HOLOMORPHIC DYNAMICS, RESIDUES, HYPEROBOLICITY
  

Algebraic Number Theory:

• ABELIAN VARIETIES OVER NUMBER FIELDS
  
• ALGEBRAIC CURVES OVER FINITE FIELDS
  
• ARITHMETIC PROPERTIES OF ALGEBRAIC VARIETIES
  
• ARAKELOV CLASS GROUPS
  
• GROUP SCHEMES