[{"publication":"Mathematical Research Letters","external_id":{"isi":["001027656000006"],"arxiv":["2108.01587"]},"title":"On type II degenerations of hyperkähler manifolds","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2108.01587"}],"issue":"1","scopus_import":"1","project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","call_identifier":"H2020"}],"arxiv":1,"citation":{"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>","ista":"Huybrechts D, Mauri M. 2023. On type II degenerations of hyperkähler manifolds. Mathematical Research Letters. 30(1), 125–141.","short":"D. Huybrechts, M. Mauri, Mathematical Research Letters 30 (2023) 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>.","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>","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."},"publication_status":"published","oa_version":"Preprint","page":"125-141","day":"21","ec_funded":1,"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."}],"status":"public","date_updated":"2024-01-16T12:00:47Z","isi":1,"article_type":"original","volume":30,"month":"06","quality_controlled":"1","publication_identifier":{"issn":["1073-2780"],"eissn":["1945-001X"]},"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"        30","date_created":"2023-07-23T22:01:14Z","department":[{"_id":"TaHa"}],"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.","date_published":"2023-06-21T00:00:00Z","author":[{"last_name":"Huybrechts","first_name":"D.","full_name":"Huybrechts, D."},{"last_name":"Mauri","id":"2cf70c34-09c1-11ed-bd8d-c34fac206130","first_name":"Mirko","full_name":"Mauri, Mirko"}],"oa":1,"_id":"13268","type":"journal_article","language":[{"iso":"eng"}],"doi":"10.4310/mrl.2023.v30.n1.a6","publisher":"International Press","year":"2023"},{"abstract":[{"lang":"eng","text":"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)\r\n  between bounded derived categories of coherent sheaves generates  Db(X)\r\n  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~\r\n  smooth, satisfying  Rπ∗(OX~)=OX ."}],"ec_funded":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"03","oa_version":"Published Version","publication_status":"published","date_updated":"2023-12-13T12:18:18Z","status":"public","title":"Homological Bondal-Orlov localization conjecture for rational singularities","file":[{"access_level":"open_access","content_type":"application/pdf","relation":"main_file","creator":"dernst","checksum":"c36241750cc5cb06890aec0ecdfee626","file_id":"14266","date_created":"2023-09-05T06:43:11Z","success":1,"date_updated":"2023-09-05T06:43:11Z","file_name":"2023_ForumMathematics_Mauri.pdf","file_size":280865}],"external_id":{"arxiv":["2212.06786"],"isi":["001041926700001"]},"publication":"Forum of Mathematics, Sigma","citation":{"mla":"Mauri, Mirko, and Evgeny Shinder. “Homological Bondal-Orlov Localization Conjecture for Rational Singularities.” <i>Forum of Mathematics, Sigma</i>, vol. 11, e66, Cambridge University Press, 2023, doi:<a href=\"https://doi.org/10.1017/fms.2023.65\">10.1017/fms.2023.65</a>.","apa":"Mauri, M., &#38; Shinder, E. (2023). Homological Bondal-Orlov localization conjecture for rational singularities. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2023.65\">https://doi.org/10.1017/fms.2023.65</a>","short":"M. Mauri, E. Shinder, Forum of Mathematics, Sigma 11 (2023).","ista":"Mauri M, Shinder E. 2023. Homological Bondal-Orlov localization conjecture for rational singularities. Forum of Mathematics, Sigma. 11, e66.","ama":"Mauri M, Shinder E. Homological Bondal-Orlov localization conjecture for rational singularities. <i>Forum of Mathematics, Sigma</i>. 2023;11. doi:<a href=\"https://doi.org/10.1017/fms.2023.65\">10.1017/fms.2023.65</a>","chicago":"Mauri, Mirko, and Evgeny Shinder. “Homological Bondal-Orlov Localization Conjecture for Rational Singularities.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2023. <a href=\"https://doi.org/10.1017/fms.2023.65\">https://doi.org/10.1017/fms.2023.65</a>.","ieee":"M. Mauri and E. Shinder, “Homological Bondal-Orlov localization conjecture for rational singularities,” <i>Forum of Mathematics, Sigma</i>, vol. 11. Cambridge University Press, 2023."},"arxiv":1,"project":[{"name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","grant_number":"101034413"}],"has_accepted_license":"1","scopus_import":"1","_id":"14239","oa":1,"author":[{"first_name":"Mirko","full_name":"Mauri, Mirko","id":"2cf70c34-09c1-11ed-bd8d-c34fac206130","last_name":"Mauri"},{"first_name":"Evgeny","full_name":"Shinder, Evgeny","last_name":"Shinder"}],"date_published":"2023-08-03T00:00:00Z","year":"2023","publisher":"Cambridge University Press","doi":"10.1017/fms.2023.65","language":[{"iso":"eng"}],"type":"journal_article","publication_identifier":{"eissn":["2050-5094"]},"quality_controlled":"1","month":"08","volume":11,"article_type":"original","isi":1,"acknowledgement":"We thank Agnieszka Bodzenta-Skibińska, Paolo Cascini, Wahei Hara, Sándor Kovács, Alexander Kuznetsov, Mircea Musta  ă, Nebojsa Pavic, Pavel Sechin, and Michael Wemyss for discussions and e-mail correspondence. We also thank the anonymous referee for the helpful comments. M.M. was supported by 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. E.S. was partially supported by the EPSRC grant EP/T019379/1 “Derived categories and algebraic K-theory of singularities”, and by the ERC Synergy grant “Modern Aspects of Geometry: Categories, Cycles and Cohomology of Hyperkähler Varieties.”\r\n\r\n","department":[{"_id":"TaHa"}],"article_number":"e66","date_created":"2023-08-27T22:01:16Z","intvolume":"        11","file_date_updated":"2023-09-05T06:43:11Z","article_processing_charge":"Yes","ddc":["510"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"}]