Twisted cscK metrics and Kähler slope stability
arXiv:0804.0414
Abstract
We introduce a cohomological obstruction to solving the constant scalar curvature Kähler (cscK) equation twisted by a semipositive form, appearing in works of Fine and Song-Tian. Geometrically this gives an obstruction for a manifold to be the base of a holomorphic submersion carrying a cscK metric in certain ``adiabatic'' classes. In turn this produces many new examples of general type threefolds with classes which do not admit a cscK representative. When the twist vanishes our obstruction extends the slope stability of Ross-Thomas to effective divisors on a Kähler manifold. Thus we find examples of non-projective slope unstable manifolds.
29 pages
References in corpus (10)
- The Kähler-Ricci flow on surfaces of positive Kodaira dimension
- Numerical characterization of the Kähler cone of a compact Kähler manifold
- On the homotopy types of compact kaehler and complex projective manifolds
- CM Stability and the Generalized Futaki Invariant I
- Unstable products of smooth curves
- Extremal metrics and K-stability (PhD thesis)
- Geometry of Kähler Metrics and Foliations by Holomorphic Discs
- Unstable Kodaira Fibrations
- Double Kodaira fibrations
- Deligne pairings and the Knudsen-Mumford expansion