Classification of non-rigid families of K3 surfaces and a finiteness theorem of Arakelov type.
Moduli spaces for linear differential equations and the Painlevé equations
A systematic construction of isomonodromic families of connections of rank two on the Riemann sphere is obtained by considering the analytic Riemann–Hilbert map , where is a moduli space of connections and , , is a moduli space for analytic data (, ordinary monodromy, Stokes matrices and links). The assumption that the fibres of (, the isomonodromic families) have dimension one, leads to ten moduli spaces . The induced Painlevé equations are computed explicitly. Except for the Painlevé VI...
Page 1