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arXiv · 1909.06924

A conjectural bound on the second Betti number for hyper-K\"ahler manifolds

Yoon-Joo Kim·Radu Laza
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Abstract

In previous work, we noted that the known cases of hyper-K\"ahler manifolds satisfy a natural condition on the LLV decomposition of the cohomology; informally, the Verbitsky component is the dominant representation in the LLV decomposition. Assuming this condition holds for all hyper-K\"ahler manifolds, we obtain an upper bound for the second Betti number in terms of the dimension.

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Yoon-Joo Kim, Radu Laza. 2019-09-16. A conjectural bound on the second Betti number for hyper-K\"ahler manifolds. https://arxiv.org/abs/1909.06924

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