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AN EFFECTIVE UPPER BOUND FOR ANTI-CANONICAL VOLUMES OF SINGULAR FANO THREEFOLDS 奇异扇形三次方反规范体积的有效上界
IF 0.9 2区 数学
Journal of the Institute of Mathematics of Jussieu Pub Date : 2024-03-08 DOI: 10.1017/s1474748024000070
Chen Jiang, Yu Zou
{"title":"AN EFFECTIVE UPPER BOUND FOR ANTI-CANONICAL VOLUMES OF SINGULAR FANO THREEFOLDS","authors":"Chen Jiang, Yu Zou","doi":"10.1017/s1474748024000070","DOIUrl":"https://doi.org/10.1017/s1474748024000070","url":null,"abstract":"<p>For a real number <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240307144005320-0828:S1474748024000070:S1474748024000070_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$0&lt;epsilon &lt;1/3$</span></span></img></span></span>, we show that the anti-canonical volume of an <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240307144005320-0828:S1474748024000070:S1474748024000070_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$epsilon $</span></span></img></span></span>-klt Fano <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240307144005320-0828:S1474748024000070:S1474748024000070_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$3$</span></span></img></span></span>-fold is at most <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240307144005320-0828:S1474748024000070:S1474748024000070_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$3,200/epsilon ^4$</span></span></img></span></span>, and the order <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240307144005320-0828:S1474748024000070:S1474748024000070_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$O(1/epsilon ^4)$</span></span></img></span></span> is sharp.</p>","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"22 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140074722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
ENERGY BOUNDS FOR MODULAR ROOTS AND THEIR APPLICATIONS 模块根的能量边界及其应用
IF 0.9 2区 数学
Journal of the Institute of Mathematics of Jussieu Pub Date : 2024-03-04 DOI: 10.1017/s1474748023000397
Bryce Kerr, Ilya D. Shkredov, Igor E. Shparlinski, Alexandru Zaharescu
{"title":"ENERGY BOUNDS FOR MODULAR ROOTS AND THEIR APPLICATIONS","authors":"Bryce Kerr, Ilya D. Shkredov, Igor E. Shparlinski, Alexandru Zaharescu","doi":"10.1017/s1474748023000397","DOIUrl":"https://doi.org/10.1017/s1474748023000397","url":null,"abstract":"<p>We generalise and improve some recent bounds for additive energies of modular roots. Our arguments use a variety of techniques, including those from additive combinatorics, algebraic number theory and the geometry of numbers. We give applications of these results to new bounds on correlations between <span>Salié</span> sums and to a new equidistribution estimate for the set of modular roots of primes.</p>","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"227 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
PERFECTING GROUP SCHEMES 完善集团计划
IF 0.9 2区 数学
Journal of the Institute of Mathematics of Jussieu Pub Date : 2024-02-16 DOI: 10.1017/s1474748024000033
Kevin Coulembier, Geordie Williamson
{"title":"PERFECTING GROUP SCHEMES","authors":"Kevin Coulembier, Geordie Williamson","doi":"10.1017/s1474748024000033","DOIUrl":"https://doi.org/10.1017/s1474748024000033","url":null,"abstract":"We initiate a systematic study of the perfection of affine group schemes of finite type over fields of positive characteristic. The main result intrinsically characterises and classifies the perfections of reductive groups and obtains a bijection with the set of classifying spaces of compact connected Lie groups topologically localised away from the characteristic. We also study the representations of perfectly reductive groups. We establish a highest weight classification of simple modules, the decomposition into blocks, and relate extension groups to those of the underlying abstract group.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"25 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139754066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
LIMIT SETS OF UNFOLDING PATHS IN OUTER SPACE 外太空极限展开路径集
IF 0.9 2区 数学
Journal of the Institute of Mathematics of Jussieu Pub Date : 2024-02-15 DOI: 10.1017/s1474748023000488
Mladen Bestvina, Radhika Gupta, Jing Tao
{"title":"LIMIT SETS OF UNFOLDING PATHS IN OUTER SPACE","authors":"Mladen Bestvina, Radhika Gupta, Jing Tao","doi":"10.1017/s1474748023000488","DOIUrl":"https://doi.org/10.1017/s1474748023000488","url":null,"abstract":"We construct an unfolding path in Outer space which does not converge in the boundary, and instead it accumulates on the entire 1-simplex of projectivized length measures on a nongeometric arational <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748023000488_inline1.png\" /> <jats:tex-math> ${mathbb R}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-tree <jats:italic>T</jats:italic>. We also show that <jats:italic>T</jats:italic> admits exactly two dual ergodic projective currents. This is the first nongeometric example of an arational tree that is neither uniquely ergodic nor uniquely ergometric.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"2 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139754126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
TRILINEAR FOURIER MULTIPLIERS ON HARDY SPACES 哈迪空间上的三线性傅里叶乘数
IF 0.9 2区 数学
Journal of the Institute of Mathematics of Jussieu Pub Date : 2024-02-15 DOI: 10.1017/s1474748023000518
Jin Bong Lee, Bae Jun Park
{"title":"TRILINEAR FOURIER MULTIPLIERS ON HARDY SPACES","authors":"Jin Bong Lee, Bae Jun Park","doi":"10.1017/s1474748023000518","DOIUrl":"https://doi.org/10.1017/s1474748023000518","url":null,"abstract":"In this paper, we obtain the <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748023000518_inline1.png\" /> <jats:tex-math> $H^{p_1}times H^{p_2}times H^{p_3}to H^p$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> boundedness for trilinear Fourier multiplier operators, which is a trilinear analogue of the multiplier theorem of Calderón and Torchinsky [4]. Our result improves the trilinear estimate in [22] by additionally assuming an appropriate vanishing moment condition, which is natural in the boundedness into the Hardy space <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748023000518_inline2.png\" /> <jats:tex-math> $H^p$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> for <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748023000518_inline3.png\" /> <jats:tex-math> $0&lt;ple 1$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"94 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139754127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
CHARACTERIZATION OF THE REDUCED PERIPHERAL SYSTEM OF LINKS 简化外围链接系统的特点
IF 0.9 2区 数学
Journal of the Institute of Mathematics of Jussieu Pub Date : 2024-02-01 DOI: 10.1017/s1474748023000543
Benjamin Audoux, Jean-Baptiste Meilhan
{"title":"CHARACTERIZATION OF THE REDUCED PERIPHERAL SYSTEM OF LINKS","authors":"Benjamin Audoux, Jean-Baptiste Meilhan","doi":"10.1017/s1474748023000543","DOIUrl":"https://doi.org/10.1017/s1474748023000543","url":null,"abstract":"<p>The reduced peripheral system was introduced by Milnor [18] in the 1950s for the study of links up to link-homotopy, that is, up to homotopies leaving distinct components disjoint; this invariant, however, fails to classify links up to link-homotopy for links of four or more components. The purpose of this paper is to show that the topological information which is detected by Milnor’s reduced peripheral system is actually 4-dimensional. The main result gives indeed a complete characterization of links having the same reduced peripheral system, in terms of ribbon solid tori in 4–space up to ribbon link-homotopy. The proof relies on an intermediate characterization given in terms of welded diagrams up to self-virtualization, hence providing a purely topological application of the combinatorial theory of welded links.</p>","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"8 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139656468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
GLOBAL HYPOELLIPTICITY OF SUMS OF SQUARES ON COMPACT MANIFOLDS 紧凑流形上平方和的全局次椭圆性
IF 0.9 2区 数学
Journal of the Institute of Mathematics of Jussieu Pub Date : 2024-01-05 DOI: 10.1017/s147474802300049x
Gabriel Araújo, Igor A. Ferra, Luis F. Ragognette
{"title":"GLOBAL HYPOELLIPTICITY OF SUMS OF SQUARES ON COMPACT MANIFOLDS","authors":"Gabriel Araújo, Igor A. Ferra, Luis F. Ragognette","doi":"10.1017/s147474802300049x","DOIUrl":"https://doi.org/10.1017/s147474802300049x","url":null,"abstract":"<p>We present necessary and sufficient conditions for an operator of the type sum of squares to be globally hypoelliptic on <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240105043019850-0091:S147474802300049X:S147474802300049X_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$T times G$</span></span></img></span></span>, where <span>T</span> is a compact Riemannian manifold and <span>G</span> is a compact Lie group. These conditions involve the global hypoellipticity of a system of vector fields on <span>G</span> and are weaker than Hörmander’s condition, while generalizing the well known Diophantine conditions on the torus. Examples of operators satisfying these conditions in the general setting are provided.</p>","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"52 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139102593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A CATEGORICAL APPROACH TO THE BAUM–CONNES CONJECTURE FOR ÉTALE GROUPOIDS 鲍姆-康内斯猜想（Baum-connes conjecture for étale groupoids）的分类方法
IF 0.9 2区 数学
Journal of the Institute of Mathematics of Jussieu Pub Date : 2024-01-02 DOI: 10.1017/s1474748023000531
Christian Bönicke, Valerio Proietti
{"title":"A CATEGORICAL APPROACH TO THE BAUM–CONNES CONJECTURE FOR ÉTALE GROUPOIDS","authors":"Christian Bönicke, Valerio Proietti","doi":"10.1017/s1474748023000531","DOIUrl":"https://doi.org/10.1017/s1474748023000531","url":null,"abstract":"<p>We consider the equivariant Kasparov category associated to an étale groupoid, and by leveraging its triangulated structure we study its localization at the ‘weakly contractible’ objects, extending previous work by R. Meyer and R. Nest. We prove the subcategory of weakly contractible objects is complementary to the localizing subcategory of projective objects, which are defined in terms of ‘compactly induced’ algebras with respect to certain proper subgroupoids related to isotropy. The resulting ‘strong’ Baum–Connes conjecture implies the classical one, and its formulation clarifies several permanence properties and other functorial statements. We present multiple applications, including consequences for the Universal Coefficient Theorem, a generalized ‘going-down’ principle, injectivity results for groupoids that are amenable at infinity, the Baum–Connes conjecture for group bundles, and a result about the invariance of <span>K</span>-groups of twisted groupoid <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231230102241472-0210:S1474748023000531:S1474748023000531_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$C^*$</span></span></img></span></span>-algebras under homotopy of twists.</p>","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"203 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139078171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
FORMALLY REGULAR RINGS AND DESCENT OF REGULARITY 形式正则环和正则性下降
IF 0.9 2区 数学
Journal of the Institute of Mathematics of Jussieu Pub Date : 2024-01-02 DOI: 10.1017/s147474802300052x
Javier Majadas, Samuel Alvite, Nerea G. Barral
{"title":"FORMALLY REGULAR RINGS AND DESCENT OF REGULARITY","authors":"Javier Majadas, Samuel Alvite, Nerea G. Barral","doi":"10.1017/s147474802300052x","DOIUrl":"https://doi.org/10.1017/s147474802300052x","url":null,"abstract":"<p>Valuation rings and perfectoid rings are examples of (usually non-Noetherian) rings that behave in some sense like regular rings. We give and study an extension of the concept of regular local rings to non-Noetherian rings so that it includes valuation and perfectoid rings and it is related to Grothendieck’s definition of formal smoothness as in the Noetherian case. For that, we have to take into account the topologies. We prove a descent theorem for regularity along flat homomorphisms (in fact for homomorphisms of finite flat dimension), extending some known results from the Noetherian to the non-Noetherian case, as well as generalizing some recent results in the non-Noetherian case, such as the descent of regularity from perfectoid rings by B. Bhatt, S. Iyengar and L. Ma.</p>","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"23 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139077691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
RIGID STABLE VECTOR BUNDLES ON HYPERKÄHLER VARIETIES OF TYPE 型超卡勒变体上的刚性稳定向量束
IF 0.9 2区 数学
Journal of the Institute of Mathematics of Jussieu Pub Date : 2023-12-22 DOI: 10.1017/s1474748023000452
Kieran G. O’Grady
{"title":"RIGID STABLE VECTOR BUNDLES ON HYPERKÄHLER VARIETIES OF TYPE","authors":"Kieran G. O’Grady","doi":"10.1017/s1474748023000452","DOIUrl":"https://doi.org/10.1017/s1474748023000452","url":null,"abstract":"We prove existence and unicity of slope-stable vector bundles on a general polarized hyperkähler (HK) variety of type <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748023000452_inline2.png\" /> <jats:tex-math> $K3^{[n]}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> with certain discrete invariants, provided the rank and the first two Chern classes of the vector bundle satisfy certain equalities. The latter hypotheses at first glance appear to be quite restrictive, but, in fact, we might have listed almost all slope-stable rigid projectively hyperholomorphic vector bundles on polarized HK varieties of type <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748023000452_inline3.png\" /> <jats:tex-math> $K3^{[n]}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> with <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748023000452_inline4.png\" /> <jats:tex-math> $20$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> moduli.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"85 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139020498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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