Journal of Differential Geometry

Twisted constant scalar curvature Kähler metrics and Kähler slope stability

Jacopo Stoppa

Full-text: Open access

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 27 January 2010

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1264601038

Digital Object Identifier
doi:10.4310/jdg/1264601038

Mathematical Reviews number (MathSciNet)
MR2581360

Zentralblatt MATH identifier
1203.32006

Citation

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. https://projecteuclid.org/euclid.jdg/1264601038


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