Yongnam Lee

Title: Simply connected surfaces of general type with vanishing geometric genus in positive characteristic via deformation theory

Abstract: The compact moduli spaces of surfaces of general type and symplectic 4-manifold give some intuitive ideas to construct simply connected surfaces of general type with vanishing geometric genus over the filed of complex numbers.  We present algebraically simply connected surfaces of general type with vanishing geometric genus in positive characteristic by using a Q-Gorenstein smoothing of two dimensional toric singularities of special type, previous constructions over the field of complex numbers, and Grothendieck's specialization theorem for the fundamental group. In order to do this, we develop the Q-Gorenstein deformation theory over a Noetherian complete regular local ring. It is a jointed work with Noboru Nakayama.