Nowadays algebraic geometry also considers much more abstract structures.
The algebra group at UiS works mainly in the realms of projective geometry, studying varieties which admit embeddings into projective spaces.
The scientists focus on the following subject areas:
- Calabi-Yau type varieties (a class of varieties on the boundary of knowledge from the point of view of classification with ample applications in other fields of mathematics)
- Fano manifolds (classical algebraic varieties studied already in 1930s)
- Moduli spaces (varieties parametrizing other objects)
- Enumerative geometry (counting curves and other objects on algebraic varieties)
- Derived categories (some abstract structures associated to algebraic varieties)
- Stability conditions (structures that permit to construct moduli spaces)
During 2014-2018 the research group hosts the project "Sheaves on
abelian varieties", funded by the Research Council of Norway and the
University of Stavanger.
