Togliatti Surface by Claudio Rocchini CC-BY-SA-3.0 

The algebraic geometry group in Genova has research interests that include: Algebraic Geometry, Complex Geometry, Geometry from Mathematical Physics, Algebraic Number Theory and Arithmetic Geometry. More specifically, some topics that are actively pursued by faculty members of this group are:

1. Geometry of complex algebraic surfaces, in particular k3 surfaces, surfaces of general type and their moduli spaces; 
2. Geometry, constructions and moduli of higher dimensional varieties in particular: irreducible symplectic manifolds, threefolds of general type, Fano varieties, and abelian varieties; 
3. The theory of abelian varieties, modular forms and their associated L-functions; 
4. Moduli spaces of sheaves on complex surfaces; quiver varieties; Fourier-Mukai and Nahm transforms; 
5. Geometry of integrable systems; bi-Hamiltonian structures; special-Kähler geometry; 
6. Geometry and applications to gauge theory and to string theories; 
7. History of mathematics in the 19th and 20th centuries; philosophical aspects of the relationship between geometry and physics; 
8. Convex geometry of Newton-Okounkov bodies together with its relation to positivity aspects in algebraic geometry and the study of syzygies of algebraic varieties.