Twisted cscK metrics and Kähler slope stability
نویسنده
چکیده
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.
منابع مشابه
Deformations of twisted cscK metrics
of the Dissertation Deformations of twisted cscK metrics
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We prove that polarised manifolds that admit a constant scalar curvature Kähler (cscK) metric satisfy a condition we call slope semistability. That is, we define the slope µ for a projective manifold and for each of its subschemes, and show that if X is cscK then µ(Z) ≤ µ(X) for all subschemes Z. This gives many examples of manifolds with Kähler classes which do not admit cscK metrics, such as ...
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We prove that polarised manifolds that admit a constant scalar curvature Kähler (cscK) metric satisfy a condition we call slope semistability. That is, we define the slope µ for a projective manifold and for each of its subschemes, and show that if X is cscK then µ(Z) ≤ µ(X) for all subschemes Z. This gives many examples of manifolds with Kähler classes which do not admit cscK metrics, such as ...
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