Ders Serisi Group actions on four-manifolds: Lecture 4,5 Tarihler 26.05.2017 - 26.05.2017 Yer IMBM Seminar Room, Boğaziçi University Alan Grup Teorisi Konular Group actions Özet Weimin Chen (University of Massachusetts Amherst) is going to give a lecture series entitled ''Group actions on 4-manifolds'' at IMBM on May 24th and May 26th. The lectures will start at 9:00. Lecture 4: Symplectic finite group actions: part II We discuss some recent new approach for studying symplectic finite group actions based on the construction of symplectic resolution, i.e., for each symplectic 4-manifold $M$ equipped with a finite symplectic $G$-action, we associate it with a symplectic 4-manifold $M_G$, which is the symplectic resolution of the symplectic orbifold $M/G$. Then the new approach will be centered around the following conjecture $\kappa^s(M_G)\leq\kappa^s(M)$ where $\kappa^s$ is the symplectic Kodaira dimension Lecture 5: Topology of symplectic Calabi-Yau G-surfaces A symplectic Calabi-Yau surface (SCY) is a symplectic 4-manifold with trivial canonical line bundle. We verify the above conjecture for the case where $M$ is a SCY, showing that in this case $M_G$ is either minimal with $\kappa^s = 0$, or $M_G$ is rational or a ruled surface over $T^2$. Furthermore, we will explain that when $M_G$ is rational or ruled, $M$ must be diffeomorphic to either a hyperelliptic surface, or $T^4$, or a $K3$ surface (on-going work), providing further evidence to the standard conjecture regarding the smooth classification of SCY. İletişim cagri.karakurt@boun.edu.tr | admin | 17.05.2017_17:06