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A Sharp Bound for the Second Betti Number of Hyperkähler Sixfolds
Let $X$ be a smooth compact irreducible hyperkähler manifold of dimension six. We prove that the second Betti number satisfies $b_2(X) \le 23$. Furthermore, we show that the third cohomology vanishes whenever $b_2(X) \ge 19$, and that all odd cohomology vanishes when $b_2(X) = 23$. If the second Che
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