@article{13268,
  abstract     = {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.},
  author       = {Huybrechts, D. and Mauri, Mirko},
  issn         = {1945-001X},
  journal      = {Mathematical Research Letters},
  number       = {1},
  pages        = {125--141},
  publisher    = {International Press},
  title        = {{On type II degenerations of hyperkähler manifolds}},
  doi          = {10.4310/mrl.2023.v30.n1.a6},
  volume       = {30},
  year         = {2023},
}

@article{14239,
  abstract     = {Given a resolution of rational singularities  π:X~→X  over a field of characteristic zero, we use a Hodge-theoretic argument to prove that the image of the functor  Rπ∗:Db(X~)→Db(X)
  between bounded derived categories of coherent sheaves generates  Db(X)
  as a triangulated category. This gives a weak version of the Bondal–Orlov localization conjecture [BO02], answering a question from [PS21]. The same result is established more generally for proper (not necessarily birational) morphisms  π:X~→X , with  X~
  smooth, satisfying  Rπ∗(OX~)=OX .},
  author       = {Mauri, Mirko and Shinder, Evgeny},
  issn         = {2050-5094},
  journal      = {Forum of Mathematics, Sigma},
  publisher    = {Cambridge University Press},
  title        = {{Homological Bondal-Orlov localization conjecture for rational singularities}},
  doi          = {10.1017/fms.2023.65},
  volume       = {11},
  year         = {2023},
}