Journal of Differential Geometry

Twisted constant scalar curvature Kähler metrics and Kähler slope stability

Jacopo Stoppa

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On a compact Kähler 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 Kähler manifold. Thus we find examples of non-projective slope unstable manifolds.

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J. Differential Geom., Volume 83, Number 3 (2009), 663-691.

First available in Project Euclid: 27 January 2010

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Stoppa, Jacopo. Twisted constant scalar curvature Kähler metrics and Kähler slope stability. J. Differential Geom. 83 (2009), no. 3, 663--691. doi:10.4310/jdg/1264601038.

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