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Beauville-Bogomolov-Fujiki Form


The Beauville-Bogomolov-Fujiki form q_X is the primitive integral quadratic form on H^2(X,Z) of an irreducible holomorphic symplectic manifold, with sign chosen to be positive on Kähler classes. For complex dimension 2n, it satisfies

 int_Xa^(2n)=c_Xq_X(a)^n,

where c_X>0 is a constant depending on X. Its signature is (3,b_2(X)-3). For a K3 surface it is the intersection form on second cohomology. A line bundle is isotropic for this form when q_X(c_1(L))=0. This condition is distinct from vanishing of its entire first Chern class.


See also

Chern Class, Intersection Form, Irreducible Holomorphic Symplectic Manifold, K3 Surface, Quadratic Form, Strong Hyper-Kaehler SYZ Conjecture

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References

Huybrechts, D. "Compact Hyperkähler Manifolds: Basic Results." Invent. Math. 135, 63-113, 1999. https://doi.org/10.1007/s002220050280.

Cite this as:

Weisstein, Eric W. "Beauville-Bogomolov-Fujiki Form." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Beauville-Bogomolov-FujikiForm.html

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