Twisted constant scalar curvature kähler metrics and kähler slope stability

Jacopo Stoppa Trinity College

Differential Geometry mathscidoc:1609.10152

Journal of Differential Geometry, 83, (3), 663-691, 2009
On a compact K¨ahler manifold we introduce a cohomological obstruction to the solvability of the constant scalar curvature (cscK) equation twisted by a semipositive form, appearing in works of Fine and Song-Tian. As a special case we find an obstruction for a manifold to be the base of a holomorphic submersion carrying a cscK metric in certain “adiabatic” classes. We apply this to find 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 K¨ahler manifold. Thus we find examples of non-projective slope unstable manifolds.
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@inproceedings{jacopo2009twisted,
  title={TWISTED CONSTANT SCALAR CURVATURE kähler METRICS AND kähler SLOPE STABILITY},
  author={Jacopo Stoppa},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911203922212791809},
  booktitle={Journal of Differential Geometry},
  volume={83},
  number={3},
  pages={663-691},
  year={2009},
}
Jacopo Stoppa. TWISTED CONSTANT SCALAR CURVATURE kähler METRICS AND kähler SLOPE STABILITY. 2009. Vol. 83. In Journal of Differential Geometry. pp.663-691. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911203922212791809.
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