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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 ℳ g pst ( S , E ) of polystable holomorphic structures ℰ with det ℰ ≅ 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, ℳ 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...

Moment-angle complexes from simplicial posets

Zhi Lü, Taras Panov (2011)

Open Mathematics

We extend the construction of moment-angle complexes to simplicial posets by associating a certain T m-space Z S to an arbitrary simplicial poset S on m vertices. Face rings ℤ[S] of simplicial posets generalise those of simplicial complexes, and give rise to new classes of Gorenstein and Cohen-Macaulay rings. Our primary motivation is to study the face rings ℤ[S] by topological methods. The space Z S has many important topological properties of the original moment-angle complex Z K associated to...

Morse index of a cyclic polygon

Gaiane Panina, Alena Zhukova (2011)

Open Mathematics

It is known that cyclic configurations of a planar polygonal linkage are critical points of the signed area function. In the paper we give an explicit formula of the Morse index for the signed area of a cyclic configuration. We show that it depends not only on the combinatorics of a cyclic configuration, but also on its metric properties.

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