Fundamental Group of the Complement to Certain Special Divisors on the Moduli Space of Points on CP^2
The goal of this diploma thesis is to understand symplectic mapping class group of rational 4-manifolds and how it changes, when the cohomology class of the symplectic form varies. For this aims, we will show that in some cases this group admits a realization as the fundamental group of the complement to certain divisor on Hilbert scheme of points on CP^2. This divisor is the locus of special constellations of points which parameterize rational complex surfaces with rational -curves on . In the paper we will describe irreducible components of this divisor and show that the loops around the components of the divisor are natural generators of the symplectic mapping class group.