{"date_published":"2020-04-15T00:00:00Z","file_date_updated":"2020-07-14T12:48:02Z","publication_identifier":{"issn":["10221824"],"eissn":["14209020"]},"date_created":"2020-04-26T22:00:44Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"type":"journal_article","publication_status":"published","ddc":["510"],"issue":"2","title":"Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces","abstract":[{"lang":"eng","text":"For any free oriented Borel–Moore homology theory A, we construct an associative product on the A-theory of the stack of Higgs torsion sheaves over a projective curve C. We show that the resulting algebra AHa0C admits a natural shuffle presentation, and prove it is faithful when A is replaced with usual Borel–Moore homology groups. We also introduce moduli spaces of stable triples, heavily inspired by Nakajima quiver varieties, whose A-theory admits an AHa0C-action. These triples can be interpreted as certain sheaves on PC(ωC⊕OC). In particular, we obtain an action of AHa0C on the cohomology of Hilbert schemes of points on T∗C."}],"external_id":{"arxiv":["1801.01429"]},"language":[{"iso":"eng"}],"year":"2020","date_updated":"2021-01-12T08:14:49Z","license":"https://creativecommons.org/licenses/by/4.0/","volume":26,"oa":1,"author":[{"last_name":"Minets","id":"3E7C5304-F248-11E8-B48F-1D18A9856A87","full_name":"Minets, Sasha","first_name":"Sasha","orcid":"0000-0003-3883-1806"}],"scopus_import":1,"day":"15","month":"04","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","article_type":"original","department":[{"_id":"TaHa"}],"citation":{"apa":"Minets, S. (2020). Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces. <i>Selecta Mathematica, New Series</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00029-020-00553-x\">https://doi.org/10.1007/s00029-020-00553-x</a>","short":"S. Minets, Selecta Mathematica, New Series 26 (2020).","ieee":"S. Minets, “Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces,” <i>Selecta Mathematica, New Series</i>, vol. 26, no. 2. Springer Nature, 2020.","mla":"Minets, Sasha. “Cohomological Hall Algebras for Higgs Torsion Sheaves, Moduli of Triples and Sheaves on Surfaces.” <i>Selecta Mathematica, New Series</i>, vol. 26, no. 2, 30, Springer Nature, 2020, doi:<a href=\"https://doi.org/10.1007/s00029-020-00553-x\">10.1007/s00029-020-00553-x</a>.","chicago":"Minets, Sasha. “Cohomological Hall Algebras for Higgs Torsion Sheaves, Moduli of Triples and Sheaves on Surfaces.” <i>Selecta Mathematica, New Series</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00029-020-00553-x\">https://doi.org/10.1007/s00029-020-00553-x</a>.","ista":"Minets S. 2020. Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces. Selecta Mathematica, New Series. 26(2), 30.","ama":"Minets S. Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces. <i>Selecta Mathematica, New Series</i>. 2020;26(2). doi:<a href=\"https://doi.org/10.1007/s00029-020-00553-x\">10.1007/s00029-020-00553-x</a>"},"intvolume":"        26","article_number":"30","quality_controlled":"1","file":[{"file_id":"7690","access_level":"open_access","date_updated":"2020-07-14T12:48:02Z","checksum":"2368c4662629b4759295eb365323b2ad","file_size":792469,"content_type":"application/pdf","relation":"main_file","file_name":"2020_SelectaMathematica_Minets.pdf","creator":"dernst","date_created":"2020-04-28T10:57:58Z"}],"publication":"Selecta Mathematica, New Series","_id":"7683","status":"public","doi":"10.1007/s00029-020-00553-x","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"publisher":"Springer Nature","oa_version":"Published Version"}