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Moduli Spaces of PU ( 2 ) -Instantons on Minimal Class VII Surfaces with b 2 = 1

Konrad Schöbel (2008)

Annales de l’institut Fourier

We describe explicitly the moduli spaces g pst ( S , E ) of polystable holomorphic structures with det 𝒦 on a rank two vector bundle E with c 1 ( E ) = c 1 ( K ) and c 2 ( E ) = 0 for all minimal class VII surfaces S with b 2 ( S ) = 1 and with respect to all possible Gauduchon metrics g . These surfaces S are non-elliptic and non-Kähler complex surfaces and have recently been completely classified. When S is a half or parabolic Inoue surface, g pst ( S , E ) is always a compact one-dimensional complex disc. When S is an Enoki surface, one obtains a complex disc with finitely...

Moduli stacks of polarized K3 surfaces in mixed characteristic

Rizov, Jordan (2006)

Serdica Mathematical Journal

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,...

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