Pub Date : 2023-01-01Epub Date: 2023-07-11DOI: 10.1007/s40879-023-00651-y
Frank Gounelas, Alexis Kouvidakis
For a general cubic fourfold with Fano variety F, we compute the Hodge numbers of the locus of lines of second type and the class of the locus 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.
{"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}
Pub Date : 2023-01-01DOI: 10.1007/s40879-023-00628-x
Naoki Koseki, Genki Ouchi
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.
{"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}
Pub Date : 2022-12-20DOI: 10.1007/s40879-023-00658-5
Anwesh Ray
{"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}
Pub Date : 2022-11-22DOI: 10.1007/s40879-023-00678-1
Benjamin Bode
{"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}
Pub Date : 2022-11-01DOI: 10.1007/s40879-022-00589-7
A. Fomenko, V. Kibkalo
{"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}
Pub Date : 2022-10-26DOI: 10.1007/s40879-022-00588-8
A. Vershik, F. Petrov
{"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}
Pub Date : 2022-10-17DOI: 10.1007/s40879-022-00587-9
A. Bolsinov, V. Matveev, S. Tabachnikov
{"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}