The hard Lefschetz theorem states that if 
is a compact Kähler manifold
of complex dimension 
with Kähler class 
, then multiplication by 
gives an isomorphism 
for 
.
Hard Lefschetz Theorem
See also
Cohomology Group, Kähler Manifold, Poincare DualityExplore with Wolfram|Alpha
References
Voisin, C. Hodge Theory and Complex Algebraic Geometry I. Cambridge, England: Cambridge University Press, 2002.Cite this as:
Weisstein, Eric W. "Hard Lefschetz Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HardLefschetzTheorem.html