Anti-self-dual orbifolds with cyclic quotient singularities

Lock, 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 -