Abstract for the talk on 20.02.2019 (11:00 h)Seminar on Nonlinear Algebra
Adam Czapliński (Universität Siegen)
Lagrangian Fibrations with designed singular fibres
20.02.2019, 11:00 h, MPI für Mathematik in den Naturwissenschaften Leipzig, G3 10 (Hörsaal)
In this talk, we study Lagrangian Fibrations with designed singular ﬁbers. The idea is to construct a K3 surface X as a minimal resolution of the singularities of a double cover Y of the plane branched along a reduced but possibly reducible singular sextic Σ. Moreover, we assume that Σ has at worst A-D-E singularities. This freeness of choosing Σ allows us to construct many examples of singular ﬁbres with various singularities. We ﬁnd an explicit description of the singular ﬁbers of the Lagrangian Fibrations f : MX(0,2H,χ) →|2H|. The results shed also some light on the correlation between the degree of the discriminant divisor Δ and the topology of the corresponding moduli space.