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Anti-self-dual orbifolds with cyclic quotient singularities

Michael T. Lock, Jeff A. Viaclovsky (2015)

Journal of the European Mathematical Society

An index theorem for the anti-self-dual deformation complex on anti-self-dual orbifolds with cyclic quotient singularities is proved. We present two applications of this theorem. The first is to compute the dimension of the deformation space of the Calderbank–Singer scalar-flat Kähler toric ALE spaces. A corollary of this is that, except for the Eguchi–Hanson metric, all of these spaces admit non-toric anti-self-dual deformations, thus yielding many new examples of anti-self-dual ALE spaces. For...

The classification of weighted projective spaces

Anthony Bahri, Matthias Franz, Dietrich Notbohm, Nigel Ray (2013)

Fundamenta Mathematicae

We obtain two classifications of weighted projective spaces: up to hoeomorphism and up to homotopy equivalence. We show that the former coincides with Al Amrani's classification up to isomorphism of algebraic varieties, and deduce the latter by proving that the Mislin genus of any weighted projective space is rigid.

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