turkmath.org

In this talk, first we will review some main concepts and techniques in the smooth and symplectic 4-manifolds theory. Then we will discuss our constructions of exotic, simply connected and symplectic 4-manifolds on the Noether line and between the Noether and half Noether lines via pencils of complex curves of genus one and via symplectic surgeries. We will also present a completely geometric way of constructing certain configurations of Kodaira’s singularities in the rational elliptic surfaces, without using any monodromy arguments.