{"title":"RDP del Pezzo surfaces with global vector fields in odd characteristic","authors":"Gebhard Martin, Claudia Stadlmayr","doi":"10.14231/ag-2024-012","DOIUrl":"https://doi.org/10.14231/ag-2024-012","url":null,"abstract":"","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141037038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Counting invariant curves: A theory of Gopakumar–Vafa invariants n for Calabi–Yau threefolds with an involution","authors":"Jim Bryan, Stephen Pietromonaco","doi":"10.14231/ag-2024-008","DOIUrl":"https://doi.org/10.14231/ag-2024-008","url":null,"abstract":"","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140085125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the local étale fundamental group of KLT threefold singularities n (with an appendix by János Kollár)","authors":"Javier Carvajal-Rojas, Axel Stäbler","doi":"10.14231/ag-2023-025","DOIUrl":"https://doi.org/10.14231/ag-2023-025","url":null,"abstract":"","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135161035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A Fano-Enriques threefold is a three-dimensional non-Gorenstein Fano variety of index 1 with at most canonical singularities. We study the birational geometry of Fano-Enriques threefolds with terminal cyclic quotient singularities. We investigate their rationality, and also provide an example of a Fano-Enriques threefold, whose pliability is 9, i.e. a Fano-Enriques threefold birationally equivalent to exactly 9 Mori fibre spaces in Sarkisov category.
{"title":"On the rationality of Fano–Enriques threefolds","authors":"Arman Sarikyan","doi":"10.14231/ag-2023-023","DOIUrl":"https://doi.org/10.14231/ag-2023-023","url":null,"abstract":"A Fano-Enriques threefold is a three-dimensional non-Gorenstein Fano variety of index 1 with at most canonical singularities. We study the birational geometry of Fano-Enriques threefolds with terminal cyclic quotient singularities. We investigate their rationality, and also provide an example of a Fano-Enriques threefold, whose pliability is 9, i.e. a Fano-Enriques threefold birationally equivalent to exactly 9 Mori fibre spaces in Sarkisov category.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135161038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We define dilatations of general schemes and study their basic properties. Dilatations of group schemes are -- in favorable cases -- again group schemes, called N'eron blowups. We give two applications to their cohomology in degree zero (integral points) and degree one (torsors): we prove a canonical Moy-Prasad isomorphism that identifies the graded pieces in the congruent filtration of $G$ with the graded pieces in its Lie algebra $mathfrak g$, and we show that many level structures on moduli stacks of $G$-bundles are encoded in torsors under N'eron blowups of $G$.
{"title":"Néron blowups and low-degree cohomological applications","authors":"Arnaud Mayeux, Timo Richarz, Matthieu Romagny","doi":"10.14231/ag-2023-026","DOIUrl":"https://doi.org/10.14231/ag-2023-026","url":null,"abstract":"We define dilatations of general schemes and study their basic properties. Dilatations of group schemes are -- in favorable cases -- again group schemes, called N'eron blowups. We give two applications to their cohomology in degree zero (integral points) and degree one (torsors): we prove a canonical Moy-Prasad isomorphism that identifies the graded pieces in the congruent filtration of $G$ with the graded pieces in its Lie algebra $mathfrak g$, and we show that many level structures on moduli stacks of $G$-bundles are encoded in torsors under N'eron blowups of $G$.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136103070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We show that a very general quartic hypersurface in $mathbb P^6 $ over a field of characteristic different from 2 does not admit a decomposition of the diagonal, hence is not retract rational. This generalizes a result of Nicaise--Ottem, who showed stable irrationality over fields of characteristic 0. To prove our result, we introduce a new cycle-theoretic obstruction that may be seen as an analogue of the motivic obstruction for rationality in characteristic zero, introduced by Nicaise--Shinder and Kontsevich--Tschinkel.
{"title":"The diagonal of quartic fivefolds","authors":"Nebojsa Pavic, Stefan Schreieder","doi":"10.14231/ag-2023-027","DOIUrl":"https://doi.org/10.14231/ag-2023-027","url":null,"abstract":"We show that a very general quartic hypersurface in $mathbb P^6 $ over a field of characteristic different from 2 does not admit a decomposition of the diagonal, hence is not retract rational. This generalizes a result of Nicaise--Ottem, who showed stable irrationality over fields of characteristic 0. To prove our result, we introduce a new cycle-theoretic obstruction that may be seen as an analogue of the motivic obstruction for rationality in characteristic zero, introduced by Nicaise--Shinder and Kontsevich--Tschinkel.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136103400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Factorization centers in dimension 2 and the Grothendieck ring of varieties","authors":"Hsueh-Yung Lin, Evgeny Shinder, Susanna Zimmermann","doi":"10.14231/ag-2023-024","DOIUrl":"https://doi.org/10.14231/ag-2023-024","url":null,"abstract":"","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135161037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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