Algebraic geometry is the study of algebraic varieties (for example, polynomial equations and their graphs). The classification of algebraic varieties, the geometry of special algebraic varieties and the description of mappings of algebraic varieties are important problems of current research interest. Algebraic geometry is closely related to differential geometry and topology, commutative algebra, and number theory. In addition to continuing faculty members Bruce Crauder, Carel Faber, Sheldon Katz, and Zhenbo Qin, the Department has had a number of visitors working in algebraic geometry. The National Science Foundation as well as the National Security Agency have provided funding for OSU research in algebraic geometry.
Faculty:
Bruce Crauder: Three-dimensional algebraic varieties, particularly
birational geometry, and degenerations of surfaces; geometry of resolutions
of some three-dimensional singularities,
higher dimensional Cremona transformations (the
birational geometry of projective spaces).
Sheldon Katz: Enumerative geometry and the interaction
of algebraic geometry with theoretical physics.
Zhenbo Qin: Complex holomorphic vector
bundles over algebraic varieties and enumerative problems in
algebraic geometry.
Carel Faber: Intersection theory on the moduli space of curves,
with specific attention to the classes that show up in enumerative geometry
problems.