Anti-self-dual orbifolds with cyclic quotient singularities
Anti-self-dual orbifolds with cyclic quotient singularities
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具有循环商奇点的反自对偶轨道折叠
DOI：
10.4171/jems/572
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Michael T. Lock
中科院分区：
文献类型：
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作者：
Jeff A. Viaclovsky;Michael T. Lock
证明了具有循环商奇点的反自对偶轨道上的反自对偶形变复形的一个指标定理。我们提出了这个定理的两个应用。第一个是计算Calderbank-Singer标量平坦Kahler环面ALE空间的变形空间的维数。由此推论，除了江口-汉森度量外，所有这些空间都允许非环面的反自对偶变形，从而产生了许多反自对偶ALE空间的新例子。对于我们的第二个应用，我们计算了任何加权射影空间$\mathbb{CP}^2_{（r，q，p）}$上的标准Bochner-Kahler度量的变形空间的维数，其中相对素数为$1 < r < q < p$。一个推论是，虽然这些度量是严格的Bochner-Kahler度量，无限多的这些承认非平凡的自对偶变形，产生一个大类的新的例子自对偶orbifold度量在某些加权射影空间。
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 Kahler 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-Kahler 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-Kahler metrics, infinitely many of these admit non-trival self-dual deformations, yielding a large class of new examples of self-dual orbifold metrics on certain weighted projective spaces.
戴德金和互反律的另一种形式
DOI：
--
发表时间：
--
期刊：
to appear in Revista Math
影响因子：
--
作者：
石田弘隆;徳永浩雄(発表者);岡睦雄;島田伊知朗;徳永浩雄;Kazuhiro Konno;Kazuhiro Konno;Kazuhiro Konno and Margarida Mendes Lopes;Kazuhiro Konno;Kazuhiro Konno;Kazuhiro Konno;K. Konno;河田成人;K. Konno and M. Mendes Lopes;Masaharu Kaneda;Tadashi Ashikaga and Ken-ichi Yoshikawa;Shigeto Kawata;Tadashi Ashikaga and Mizuho Ishizaka
通讯作者：
Tadashi Ashikaga and Mizuho Ishizaka