Author

Shi-Hao Wang

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Preprint Oct 2026

A Sharp Bound for the Second Betti Number of Hyperk\"ahler Sixfolds

Let $X$ be a smooth compact irreducible hyperk\"ahler 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 Chern class lies in t...

Jie Fu, Bin Wang, Shi-Hao Wang et al. · 0 citations

Preprint Oct 2026

A Proof of Mongardi's Conjecture on Finite Symplectic Group Actions on Hyperk\"ahler Manifolds of $K3^{[n]}$ Type

Let a finite group act faithfully by symplectic automorphisms on a manifold of $K3^{[n]}$ type for $n\geq2$. We prove Mongardi's conjecture that the strict inequality $\mathrm{rk}(S)+\ell(A_S)<24$ holds for its associated Leech coinvariant lattice $S$. The converse was already proved independently by Huybrechts and Mon...

Jie Fu, Shi-Hao Wang, Zhi-Wei Zheng · 0 citations