Open Access
November 2009 Twisted constant scalar curvature Kähler metrics and Kähler slope stability
Jacopo Stoppa
J. Differential Geom. 83(3): 663-691 (November 2009). DOI: 10.4310/jdg/1264601038


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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Jacopo Stoppa. "Twisted constant scalar curvature Kähler metrics and Kähler slope stability." J. Differential Geom. 83 (3) 663 - 691, November 2009.


Published: November 2009
First available in Project Euclid: 27 January 2010

zbMATH: 1203.32006
MathSciNet: MR2581360
Digital Object Identifier: 10.4310/jdg/1264601038

Rights: Copyright © 2009 Lehigh University

Vol.83 • No. 3 • November 2009
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