# Anti-self-dual orbifolds with cyclic quotient singularities

Michael T. Lock; Jeff A. Viaclovsky

Journal of the European Mathematical Society (2015)

- Volume: 017, Issue: 11, page 2805-2842
- ISSN: 1435-9855

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topLock, Michael T., and Viaclovsky, Jeff A.. "Anti-self-dual orbifolds with cyclic quotient singularities." Journal of the European Mathematical Society 017.11 (2015): 2805-2842. <http://eudml.org/doc/277657>.

@article{Lock2015,

abstract = {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 our second application, we compute the dimension of the deformation space of the canonical Bochner-Kähler metric on any weighted projective space $\mathbb \{CP\}^2_\{(r,q,p)\}$ for relatively prime integers $1 < r < q < p$. A corollary of this is that, while these metrics are rigid as Bochner–Kähler metrics, infinitely many of these admit non-trivial self-dual deformations, yielding a large class of new examples of self-dual orbifold metrics on certain weighted projective spaces.},

author = {Lock, Michael T., Viaclovsky, Jeff A.},

journal = {Journal of the European Mathematical Society},

keywords = {anti-self-dual metrics; index theory; orbifolds; anti-self-dual metrics; index theory; orbifolds},

language = {eng},

number = {11},

pages = {2805-2842},

publisher = {European Mathematical Society Publishing House},

title = {Anti-self-dual orbifolds with cyclic quotient singularities},

url = {http://eudml.org/doc/277657},

volume = {017},

year = {2015},

}

TY - JOUR

AU - Lock, Michael T.

AU - Viaclovsky, Jeff A.

TI - Anti-self-dual orbifolds with cyclic quotient singularities

JO - Journal of the European Mathematical Society

PY - 2015

PB - European Mathematical Society Publishing House

VL - 017

IS - 11

SP - 2805

EP - 2842

AB - 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 our second application, we compute the dimension of the deformation space of the canonical Bochner-Kähler metric on any weighted projective space $\mathbb {CP}^2_{(r,q,p)}$ for relatively prime integers $1 < r < q < p$. A corollary of this is that, while these metrics are rigid as Bochner–Kähler metrics, infinitely many of these admit non-trivial self-dual deformations, yielding a large class of new examples of self-dual orbifold metrics on certain weighted projective spaces.

LA - eng

KW - anti-self-dual metrics; index theory; orbifolds; anti-self-dual metrics; index theory; orbifolds

UR - http://eudml.org/doc/277657

ER -

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