---
_id: '13268'
abstract:
- lang: eng
  text: 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 [10] and independently
    by Soldatenkov [18], while it is immediate for type III degenerations. Our arguments
    are close in spirit to a recent paper by Harder [8] proving similar results for
    the restrictive class of good degenerations.
acknowledgement: 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.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: D.
  full_name: Huybrechts, D.
  last_name: Huybrechts
- first_name: Mirko
  full_name: Mauri, Mirko
  id: 2cf70c34-09c1-11ed-bd8d-c34fac206130
  last_name: Mauri
citation:
  ama: Huybrechts D, Mauri M. On type II degenerations of hyperkähler manifolds. <i>Mathematical
    Research Letters</i>. 2023;30(1):125-141. doi:<a href="https://doi.org/10.4310/mrl.2023.v30.n1.a6">10.4310/mrl.2023.v30.n1.a6</a>
  apa: Huybrechts, D., &#38; Mauri, M. (2023). On type II degenerations of hyperkähler
    manifolds. <i>Mathematical Research Letters</i>. International Press. <a href="https://doi.org/10.4310/mrl.2023.v30.n1.a6">https://doi.org/10.4310/mrl.2023.v30.n1.a6</a>
  chicago: Huybrechts, D., and Mirko Mauri. “On Type II Degenerations of Hyperkähler
    Manifolds.” <i>Mathematical Research Letters</i>. International Press, 2023. <a
    href="https://doi.org/10.4310/mrl.2023.v30.n1.a6">https://doi.org/10.4310/mrl.2023.v30.n1.a6</a>.
  ieee: D. Huybrechts and M. Mauri, “On type II degenerations of hyperkähler manifolds,”
    <i>Mathematical Research Letters</i>, vol. 30, no. 1. International Press, pp.
    125–141, 2023.
  ista: Huybrechts D, Mauri M. 2023. On type II degenerations of hyperkähler manifolds.
    Mathematical Research Letters. 30(1), 125–141.
  mla: Huybrechts, D., and Mirko Mauri. “On Type II Degenerations of Hyperkähler Manifolds.”
    <i>Mathematical Research Letters</i>, vol. 30, no. 1, International Press, 2023,
    pp. 125–41, doi:<a href="https://doi.org/10.4310/mrl.2023.v30.n1.a6">10.4310/mrl.2023.v30.n1.a6</a>.
  short: D. Huybrechts, M. Mauri, Mathematical Research Letters 30 (2023) 125–141.
date_created: 2023-07-23T22:01:14Z
date_published: 2023-06-21T00:00:00Z
date_updated: 2024-01-16T12:00:47Z
day: '21'
department:
- _id: TaHa
doi: 10.4310/mrl.2023.v30.n1.a6
ec_funded: 1
external_id:
  arxiv:
  - '2108.01587'
  isi:
  - '001027656000006'
intvolume: '        30'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2108.01587
month: '06'
oa: 1
oa_version: Preprint
page: 125-141
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: Mathematical Research Letters
publication_identifier:
  eissn:
  - 1945-001X
  issn:
  - 1073-2780
publication_status: published
publisher: International Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: On type II degenerations of hyperkähler manifolds
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 30
year: '2023'
...