Huybrechts, D.; Mauri, MirkoISTA
We give a simple argument to prove Nagai’s conjecture for type II degenerations of compact hyperkähler manifolds and cohomology classes of middle degree. Under an additional assumption, the techniques yield the conjecture in arbitrary degree. This would complete the proof of Nagai’s conjecture in general, as it was proved already for type I degenerations by Kollár, Laza, Saccà, and Voisin  and independently by Soldatenkov , while it is immediate for type III degenerations. Our arguments are close in spirit to a recent paper by Harder  proving similar results for the restrictive class of good degenerations.
Mathematical Research Letters
The first author is supported by the ERC Synergy Grant HyperK. The second author is supported by the Max Planck Institute for Mathematics and the Institute of Science and Technology Austria. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413.
Huybrechts D, Mauri M. On type II degenerations of hyperkähler manifolds. Mathematical Research Letters. 2023;30(1):125-141. doi:10.4310/mrl.2023.v30.n1.a6
Huybrechts, D., & Mauri, M. (2023). On type II degenerations of hyperkähler manifolds. Mathematical Research Letters. International Press. https://doi.org/10.4310/mrl.2023.v30.n1.a6
Huybrechts, D., and Mirko Mauri. “On Type II Degenerations of Hyperkähler Manifolds.” Mathematical Research Letters. International Press, 2023. https://doi.org/10.4310/mrl.2023.v30.n1.a6.
D. Huybrechts and M. Mauri, “On type II degenerations of hyperkähler manifolds,” Mathematical Research Letters, vol. 30, no. 1. International Press, pp. 125–141, 2023.
Huybrechts D, Mauri M. 2023. On type II degenerations of hyperkähler manifolds. Mathematical Research Letters. 30(1), 125–141.
Huybrechts, D., and Mirko Mauri. “On Type II Degenerations of Hyperkähler Manifolds.” Mathematical Research Letters, vol. 30, no. 1, International Press, 2023, pp. 125–41, doi:10.4310/mrl.2023.v30.n1.a6.