Moduli of vector bundles on projective surfaces: some basic results.
We show that the moduli space of polarized irreducible symplectic manifolds of -type, of fixed polarization type, is not always connected. This can be derived as a consequence of Eyal Markman’s characterization of polarized parallel-transport operators of -type.
We describe explicitly the moduli spaces of polystable holomorphic structures with on a rank two vector bundle with and for all minimal class VII surfaces with and with respect to all possible Gauduchon metrics . These surfaces are non-elliptic and non-Kähler complex surfaces and have recently been completely classified. When is a half or parabolic Inoue surface, is always a compact one-dimensional complex disc. When is an Enoki surface, one obtains a complex disc with finitely...
2000 Mathematics Subject Classification: 14J28, 14D22.In this note we define moduli stacks of (primitively) polarized K3 spaces. We show that they are representable by Deligne-Mumford stacks over Spec(Z). Further, we look at K3 spaces with a level structure. Our main result is that the moduli functors of K3 spaces with a primitive polarization of degree 2d and a level structure are representable by smooth algebraic spaces over open parts of Spec(Z). To do this we use ideas of Grothendieck, Deligne,...
We generalize L. J. Mordell’s construction of cubic surfaces for which the Hasse principle fails.