{"title":"On some invariants of cubic fourfolds.","authors":"Frank Gounelas, Alexis Kouvidakis","doi":"10.1007/s40879-023-00651-y","DOIUrl":"10.1007/s40879-023-00651-y","url":null,"abstract":"<p><p>For a general cubic fourfold <math><mrow><mi>X</mi><mo>⊂</mo><msup><mrow><mi>P</mi></mrow><mn>5</mn></msup></mrow></math> with Fano variety <i>F</i>, we compute the Hodge numbers of the locus <math><mrow><mi>S</mi><mo>⊂</mo><mi>F</mi></mrow></math> of lines of second type and the class of the locus <math><mrow><mi>V</mi><mo>⊂</mo><mi>F</mi></mrow></math> of triple lines, using the description of the latter in terms of flag varieties. We also give an upper bound of 6 for the degree of irrationality of the Fano scheme of lines of any smooth cubic hypersurface.</p>","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":"9 3","pages":"58"},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10335978/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9813430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Perverse schobers and Orlov equivalences.","authors":"Naoki Koseki, Genki Ouchi","doi":"10.1007/s40879-023-00628-x","DOIUrl":"https://doi.org/10.1007/s40879-023-00628-x","url":null,"abstract":"<p><p>A perverse schober is a categorification of a perverse sheaf proposed by Kapranov-Schechtman. In this paper, we construct examples of perverse schobers on the Riemann sphere, which categorify the intersection complexes of natural local systems arising from the mirror symmetry for Calabi-Yau hypersurfaces. The Orlov equivalence plays a key role for the construction.</p>","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":"9 2","pages":"32"},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10147795/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9400674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the distribution of Alexander polynomials in certain families of closed braids","authors":"Anwesh Ray","doi":"10.1007/s40879-023-00658-5","DOIUrl":"https://doi.org/10.1007/s40879-023-00658-5","url":null,"abstract":"","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49479060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"All links are semiholomorphic","authors":"Benjamin Bode","doi":"10.1007/s40879-023-00678-1","DOIUrl":"https://doi.org/10.1007/s40879-023-00678-1","url":null,"abstract":"","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49064254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Topology of Liouville foliations of integrable billiards on table-complexes","authors":"A. Fomenko, V. Kibkalo","doi":"10.1007/s40879-022-00589-7","DOIUrl":"https://doi.org/10.1007/s40879-022-00589-7","url":null,"abstract":"","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":"8 1","pages":"1392 - 1423"},"PeriodicalIF":0.6,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48205435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Central measures of continuous graded graphs: the case of distinct frequencies","authors":"A. Vershik, F. Petrov","doi":"10.1007/s40879-022-00588-8","DOIUrl":"https://doi.org/10.1007/s40879-022-00588-8","url":null,"abstract":"","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":"8 1","pages":"481 - 493"},"PeriodicalIF":0.6,"publicationDate":"2022-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48250557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Editors’ foreword for the special issue “New Developments in Integrable Systems”","authors":"A. Bolsinov, V. Matveev, S. Tabachnikov","doi":"10.1007/s40879-022-00587-9","DOIUrl":"https://doi.org/10.1007/s40879-022-00587-9","url":null,"abstract":"","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":"8 1","pages":"1307 - 1308"},"PeriodicalIF":0.6,"publicationDate":"2022-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47271613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}