Pub Date : 2023-11-09DOI: 10.1007/s40879-023-00702-4
Ugo Bruzzo, William D. Montoya
Abstract We continue our study of the Noether–Lefschetz loci in toric varieties and investigate deformation of pairs ( V , X ) where V is a complete intersection subvariety and X a quasi-smooth hypersurface in a simplicial projective toric variety $$mathbb {P}_{Sigma }^{2k+1}$$ PΣ2k+1 , with $$Vsubset X$$ V⊂X . The hypersurface X is supposed to be of Macaulay type , which means that its toric Jacobian ideal is Cox–Gorenstein, a property that generalizes the notion of Gorenstein ideal in the standard polynomial ring. Under some assumptions, we prove that the class $$lambda _Vin H^{k,k}(X)$$ λV∈Hk,k(X) deforms to an algebraic class if and only if it remains of type ( k , k ). Actually we prove that locally the Noether–Lefschetz locus is an irreducible component of a suitable Hilbert scheme. This generalizes Theorem 4.2 in our previous work (Bruzzo and Montoya 15(2):682–694, 2021) and the main theorem proved by Dan (in: Analytic and Algebraic Geometry. Hindustan Book Agency, New Delhi, pp 107–115, 2017).
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Pub Date : 2023-11-08DOI: 10.1007/s40879-023-00704-2
Debopam Chakraborty, Vinodkumar Ghale
{"title":"Size of the 2-Selmer groups for Heronian elliptic curves","authors":"Debopam Chakraborty, Vinodkumar Ghale","doi":"10.1007/s40879-023-00704-2","DOIUrl":"https://doi.org/10.1007/s40879-023-00704-2","url":null,"abstract":"","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":" 27","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135341439","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 : 2023-11-06DOI: 10.1007/s40879-023-00697-y
Daniel Devine, Gurpreet Singh
{"title":"Existence and boundary behaviour of radial solutions for weighted elliptic systems with gradient terms","authors":"Daniel Devine, Gurpreet Singh","doi":"10.1007/s40879-023-00697-y","DOIUrl":"https://doi.org/10.1007/s40879-023-00697-y","url":null,"abstract":"","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":"19 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135589504","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 : 2023-11-02DOI: 10.1007/s40879-023-00699-w
Xavier Roulleau
{"title":"On the dynamics of the line operator $$Lambda _{{2},{3}}$$ on some arrangements of six lines","authors":"Xavier Roulleau","doi":"10.1007/s40879-023-00699-w","DOIUrl":"https://doi.org/10.1007/s40879-023-00699-w","url":null,"abstract":"","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":"18 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135973721","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 : 2023-10-30DOI: 10.1007/s40879-023-00698-x
Pavel Gvozdevsky
{"title":"Bounded reduction for Chevalley groups of types $$E_6$$ and $$E_7$$","authors":"Pavel Gvozdevsky","doi":"10.1007/s40879-023-00698-x","DOIUrl":"https://doi.org/10.1007/s40879-023-00698-x","url":null,"abstract":"","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":"38 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136104663","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 : 2023-10-30DOI: 10.1007/s40879-023-00701-5
Lewis Stanton
Abstract We generalise the fold map for the wedge sum and use this to give a loop space decomposition of topological spaces with a high degree of symmetry. This is applied to polyhedral products to give a loop space decomposition of polyhedral products associated to families of graphs.
{"title":"Loop space decompositions of highly symmetric spaces with applications to polyhedral products","authors":"Lewis Stanton","doi":"10.1007/s40879-023-00701-5","DOIUrl":"https://doi.org/10.1007/s40879-023-00701-5","url":null,"abstract":"Abstract We generalise the fold map for the wedge sum and use this to give a loop space decomposition of topological spaces with a high degree of symmetry. This is applied to polyhedral products to give a loop space decomposition of polyhedral products associated to families of graphs.","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":"247 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136102643","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 : 2023-10-30DOI: 10.1007/s40879-023-00700-6
Benjamin Schmidt
{"title":"Sheaves of low rank in three-dimensional projective space","authors":"Benjamin Schmidt","doi":"10.1007/s40879-023-00700-6","DOIUrl":"https://doi.org/10.1007/s40879-023-00700-6","url":null,"abstract":"","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":"24 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136023233","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 : 2023-10-19DOI: 10.1007/s40879-023-00694-1
Davide Mattiolo, Giuseppe Mazzuoccolo, Jozef Rajník, Gloria Tabarelli
{"title":"On d-dimensional nowhere-zero r-flows on a graph","authors":"Davide Mattiolo, Giuseppe Mazzuoccolo, Jozef Rajník, Gloria Tabarelli","doi":"10.1007/s40879-023-00694-1","DOIUrl":"https://doi.org/10.1007/s40879-023-00694-1","url":null,"abstract":"","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135729041","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 : 2023-10-12DOI: 10.1007/s40879-023-00695-0
Paul Thomas Young
{"title":"Global series for height 1 multiple zeta functions","authors":"Paul Thomas Young","doi":"10.1007/s40879-023-00695-0","DOIUrl":"https://doi.org/10.1007/s40879-023-00695-0","url":null,"abstract":"","PeriodicalId":44725,"journal":{"name":"European Journal of Mathematics","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135968705","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}
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