Scalar-flat Kähler Surfaces of All Genera
نویسندگان
چکیده
Let (M,J) be a compact complex 2-manifold which which admits a Kähler metric for which the integral of the scalar curvature is nonnegative. Also suppose that M does not admit a Ricci-flat Kähler metric. Then if M is blown up at sufficiently many points, the resulting complex surface (M̃ , J̃) admits Kähler metrics with scalar curvature identically equal to zero. This proves Conjecture 1 of [16]. ∗Supported in part by NSF grant DMS 92-04093.
منابع مشابه
Kähler Metrics of Constant Scalar Curvature on Hirzebruch Surfaces
It is shown that a Hirzebruch surface admits a Kähler metric (possibly indefinite) of constant scalar curvature if and only if its degree equals zero. There have been many extensive studies for positive-definite Kähler metrics of constant scalar curvature, especially, Kähler Einstein metrics and scalar-flat Kähler metrics, on existence, uniqueness, obstructions, and relationships with other not...
متن کاملScalar Flat Kähler Metrics on Affine Bundles over CP 1 3 2 Preliminary computations for Hirzebruch surfaces
We show that the total space of any affine C-bundle over CP with negative degree admits an ALE scalar-flat Kähler metric. Here the degree of an affine bundle means the negative of the self-intersection number of the section at infinity in a natural compactification of the bundle, and so for line bundles it agrees with the usual notion of the degree.
متن کاملJ un 2 00 6 KÄHLER MANIFOLDS ADMITTING A FLAT COMPLEX CONFORMAL CONNECTION
We prove that any Kähler manifold admitting a flat complex conformal connection is a Bochner-Kähler manifold with special scalar distribution and zero geometric constants. Applying the local structural theorem for such manifolds we obtain a complete description of the Kähler manifolds under consideration.
متن کاملSelf-dual metrics on toric 4-manifolds: Extending the Joyce construction
Toric geometry studies manifolds M2n acted on effectively by a torus of half their dimension, T . Joyce shows that for such a 4-manifold sufficient conditions for a conformal class of metrics on the free part of the action to be self-dual can be given by a pair of linear ODEs and gives criteria for a metric in this class to extend to the degenerate orbits. Joyce and Calderbank-Pedersen use this...
متن کاملToric Anti-self-dual 4-manifolds via Complex Geometry
Using the twistor correspondence, this article gives a oneto-one correspondence between germs of toric anti-self-dual conformal classes and certain holomorphic data determined by the induced action on twistor space. Recovering the metric from the holomorphic data leads to the classical problem of prescribing the Čech coboundary of 0-cochains on an elliptic curve covered by two annuli. The class...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1994