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Closed binomial edge ideals 封闭二项式边理想
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2023-08-30 DOI: 10.1515/crelle-2023-0048
I. Peeva
{"title":"Closed binomial edge ideals","authors":"I. Peeva","doi":"10.1515/crelle-2023-0048","DOIUrl":"https://doi.org/10.1515/crelle-2023-0048","url":null,"abstract":"Abstract We prove a conjecture by Ene, Herzog, and Hibi (2011) that the Betti numbers of the binomial edge ideal J G {J_{G}} of a closed graph G coincide with the Betti numbers of its lex initial ideal M G {M_{G}} . We describe the Betti numbers of the ideal M G {M_{G}} .","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75107565","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}
引用次数: 0
Comparing the Kirwan and noncommutative resolutions of quotient varieties 比较商变量的柯湾分辨和非交换分辨
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2023-07-22 DOI: 10.1515/crelle-2023-0024
S. Spenko, Michel van den Bergh
{"title":"Comparing the Kirwan and noncommutative resolutions of quotient varieties","authors":"S. Spenko, Michel van den Bergh","doi":"10.1515/crelle-2023-0024","DOIUrl":"https://doi.org/10.1515/crelle-2023-0024","url":null,"abstract":"Abstract Let a reductive group G act on a smooth variety X such that a good quotient X / / G {X/!!/G} exists. We show that the derived category of a noncommutative crepant resolution (NCCR) of X / / G {X/!!/G} , obtained from a G-equivariant vector bundle on X, can be embedded in the derived category of the (canonical, stacky) Kirwan resolution of X / / G {X/!!/G} . In fact, the embedding can be completed to a semi-orthogonal decomposition in which the other parts are all derived categories of Azumaya algebras over smooth Deligne–Mumford stacks.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86559561","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}
引用次数: 0
A nonexistence result for rotating mean curvature flows in ℝ4 一个关于旋转平均曲率流的不存在性结果
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2023-06-27 DOI: 10.1515/crelle-2023-0039
Wenkui Du, Robert Haslhofer
{"title":"A nonexistence result for rotating mean curvature flows in ℝ4","authors":"Wenkui Du, Robert Haslhofer","doi":"10.1515/crelle-2023-0039","DOIUrl":"https://doi.org/10.1515/crelle-2023-0039","url":null,"abstract":"Abstract Some worrisome potential singularity models for the mean curvature flow are rotating ancient flows, i.e. ancient flows whose tangent flow at - ∞ {-infty} is a cylinder ℝ k × S n - k {mathbb{R}^{k}times S^{n-k}} and that are rotating within the ℝ k {mathbb{R}^{k}} -factor. We note that while the ℝ k {mathbb{R}^{k}} -factor, i.e. the axis of the cylinder, is unique by the fundamental work of Colding-Minicozzi, the uniqueness of tangent flows by itself does not provide any information about rotations within the ℝ k {mathbb{R}^{k}} -factor. In the present paper, we rule out rotating ancient flows among all ancient noncollapsed flows in ℝ 4 {mathbb{R}^{4}} .","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78299100","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}
引用次数: 6
Ample line bundles and generation time 充足的线束和生成时间
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2023-06-27 DOI: 10.1515/crelle-2023-0036
Noah Olander
{"title":"Ample line bundles and generation time","authors":"Noah Olander","doi":"10.1515/crelle-2023-0036","DOIUrl":"https://doi.org/10.1515/crelle-2023-0036","url":null,"abstract":"Abstract We prove that if X is a regular quasi-projective variety of dimension d, the set of line bundles { 𝒪 X ⁢ ( n ) } n ∈ ℤ {{mathcal{O}_{X}(n)}_{nin{mathbb{Z}}}} generates the bounded derived category of X in d steps. This proves new cases of a conjecture of Orlov as well as a conjecture of Elagin and Lunts.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76955671","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}
引用次数: 0
Supersingular elliptic curves over ℤ𝑝-extensions 超奇异椭圆曲线在0𝑝-extensions上
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2023-06-15 DOI: 10.1515/crelle-2023-0029
M. Çiperiani
{"title":"Supersingular elliptic curves over ℤ𝑝-extensions","authors":"M. Çiperiani","doi":"10.1515/crelle-2023-0029","DOIUrl":"https://doi.org/10.1515/crelle-2023-0029","url":null,"abstract":"Abstract Let E / Q mathrm{E}/mathbb{Q} be an elliptic curve and 𝑝 a prime of supersingular reduction for E mathrm{E} . Consider a quadratic extension L / Q p L/mathbb{Q}_{p} and the corresponding anticyclotomic Z p mathbb{Z}_{p} -extension L ∞ / L L_{infty}/L . We analyze the structure of the points E ⁢ ( L ∞ ) mathrm{E}(L_{infty}) and describe two global implications of our results.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83151223","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}
引用次数: 0
𝐾-invariant Hilbert modules and singular vector bundles on bounded symmetric domains 𝐾-invariant有界对称域上的Hilbert模与奇异向量束
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2023-04-29 DOI: 10.1515/crelle-2023-0015
H. Upmeier
{"title":"𝐾-invariant Hilbert modules and singular vector bundles on bounded symmetric domains","authors":"H. Upmeier","doi":"10.1515/crelle-2023-0015","DOIUrl":"https://doi.org/10.1515/crelle-2023-0015","url":null,"abstract":"Abstract We show that the “eigenbundle” (localization bundle) of certain Hilbert modules over bounded symmetric domains of rank 𝑟 is a “singular” vector bundle (linearly fibred complex analytic space) which decomposes as a stratified sum of homogeneous vector bundles along a canonical stratification of length r + 1 r+1 . The fibres are realized in terms of representation theory on the normal space of the strata.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83131149","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}
引用次数: 0
Mabuchi geometry of big cohomology classes 大上同调类的Mabuchi几何
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2023-04-27 DOI: 10.1515/crelle-2023-0019
Mingchen Xia
{"title":"Mabuchi geometry of big cohomology classes","authors":"Mingchen Xia","doi":"10.1515/crelle-2023-0019","DOIUrl":"https://doi.org/10.1515/crelle-2023-0019","url":null,"abstract":"Abstract Let X be a compact Kähler manifold. Fix a big ( 1 , 1 ) {(1,1)} -cohomology class α with smooth representative θ. We study the spaces ℰ p ⁢ ( X , θ ) {mathcal{E}^{p}(X,theta)} of finite energy Kähler potentials for each p ≥ 1 {pgeq 1} . We define a metric d p {d_{p}} without using the Finsler geometry nor solving Monge–Ampère-type equations. This construction generalizes the usual d p {d_{p}} -metric defined for an ample class.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80417184","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}
引用次数: 0
A new parametrization for ideal classes in rings defined by binary forms, and applications 由二元形式定义的环上理想类的一种新的参数化方法及其应用
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2023-03-28 DOI: 10.1515/crelle-2023-0006
A. Swaminathan
{"title":"A new parametrization for ideal classes in rings defined by binary forms, and applications","authors":"A. Swaminathan","doi":"10.1515/crelle-2023-0006","DOIUrl":"https://doi.org/10.1515/crelle-2023-0006","url":null,"abstract":"Abstract We give a parametrization of square roots of the ideal class of the inverse different of rings defined by binary forms in terms of the orbits of a coregular representation. This parametrization, which can be construed as a new integral model of a “higher composition law” discovered by Bhargava and generalized by Wood, was the missing ingredient needed to solve a range of previously intractable open problems concerning distributions of class groups, Selmer groups, and related objects. For instance, in this paper, we apply the parametrization to bound the average size of the 2-class group in families of number fields defined by binary n-ic forms, where n ≥ 3 {ngeq 3} is an arbitrary integer, odd or even; in the paper [A. Swaminathan, Most integral odd-degree binary forms fail to properly represent a square, preprint 2020], we applied it to prove that most integral odd-degree binary forms fail to primitively represent a square; and in the paper [M. Bhargava, A. Shankar and A. Swaminathan, The second moment of the size of the 2-Selmer group of elliptic curves, preprint 2021], joint with Bhargava and Shankar, we applied it to bound the second moment of the size of the 2-Selmer group of elliptic curves.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81604211","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}
引用次数: 1
A twistor transform and normal forms for Cauchy Riemann structures 柯西黎曼结构的扭或变换和范式
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2023-03-25 DOI: 10.1515/crelle-2023-0002
J. Bland, T. Duchamp
{"title":"A twistor transform and normal forms for Cauchy Riemann structures","authors":"J. Bland, T. Duchamp","doi":"10.1515/crelle-2023-0002","DOIUrl":"https://doi.org/10.1515/crelle-2023-0002","url":null,"abstract":"Abstract We use Hitchin’s twistor transform for two-dimensional projective structures to obtain normal coordinates in a pseudoconcave neighbourhood of an O ⁢ ( 1 ) mathcal{O}(1) rational curve; in the construction, we present every such neighbourhood as Q D / F Q_{mathbb{D}}/mathcal{F} for some holomorphic foliation ℱ, where Q D Q_{mathbb{D}} is an open neighbourhood in the standard quadric Q ⊂ P 2 × P 2 Qsubsetmathbb{P}^{2}timesmathbb{P}^{2} . As a consequence of the normal coordinates, we obtain a new normal form for Cauchy Riemann structures on the three-sphere that are isotopic to the standard one. We end the paper with explicit calculations for the cases arising from deformations of the normal isolated singularities X ⁢ Y = Z n XY=Z^{n} .","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74522351","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}
引用次数: 0
The relative Bogomolov conjecture for fibered products of elliptic curves 椭圆曲线纤维制品的相对Bogomolov猜想
IF 1.5 1区 数学
Journal fur die Reine und Angewandte Mathematik Pub Date : 2023-01-27 DOI: 10.1515/crelle-2022-0082
L. Kühne
{"title":"The relative Bogomolov conjecture for fibered products of elliptic curves","authors":"L. Kühne","doi":"10.1515/crelle-2022-0082","DOIUrl":"https://doi.org/10.1515/crelle-2022-0082","url":null,"abstract":"Abstract We deduce an analogue of the Bogomolov conjecture for non-degenerate subvarieties in fibered products of families of elliptic curves from the author’s recent theorem on equidistribution in families of abelian varieties. This generalizes results of DeMarco and Mavraki and improves certain results of Manin–Mumford type proven by Masser and Zannier to results of Bogomolov type, yielding the first results of this type for subvarieties of relative dimension > 1 {>1} in families of abelian varieties with trivial trace.","PeriodicalId":54896,"journal":{"name":"Journal fur die Reine und Angewandte Mathematik","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87437477","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}
引用次数: 0
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