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Pacific Journal of Mathematics最新文献

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The unit signature rank deficiency is unbounded over cyclotomic fields 单位签名秩缺乏性在切环场上无界
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-11-10 DOI: 10.2140/pjm.2021.314.259
D. Dummit, H. Kisilevsky
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引用次数: 2
On the Chow groups of a biquaternionSeveri–Brauer variety 双四元数severi - brauer品种的Chow群
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-10-31 DOI: 10.2140/pjm.2022.321.359
Eoin Mackall
{"title":"On the Chow groups of a biquaternion\u0000Severi–Brauer variety","authors":"Eoin Mackall","doi":"10.2140/pjm.2022.321.359","DOIUrl":"https://doi.org/10.2140/pjm.2022.321.359","url":null,"abstract":"We provide an alternative proof that the Chow group of $1$-cycles on a Severi--Brauer variety associated to a biquaternion division algebra is torsion-free. There are three proofs of this result in the literature, all of which are due to Karpenko and rely on a clever use of $K$-theory. The proof that we give here, by contrast, is geometric and uses degenerations of quartic elliptic normal curves.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45818265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Ostrowski quotients for finite extensions of number fields 数域有限扩展的Ostrowski商
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-10-31 DOI: 10.2140/pjm.2022.321.415
Ehsan Shahoseini, A. Rajaei, A. Maarefparvar
{"title":"Ostrowski quotients for finite extensions of number fields","authors":"Ehsan Shahoseini, A. Rajaei, A. Maarefparvar","doi":"10.2140/pjm.2022.321.415","DOIUrl":"https://doi.org/10.2140/pjm.2022.321.415","url":null,"abstract":"For $L/K$ a finite Galois extension of number fields, the relative P'olya group $Po(L/K)$ coincides with the group of strongly ambiguous ideal classes in $L/K$. In this paper, using a well known exact sequence related to $Po(L/K)$, in the works of Brumer-Rosen and Zantema, we find short proofs for some classical results in the literatur. Then we define the ``Ostrowski quotient'' $Ost(L/K)$ as the cokernel of the capitulation map into $Po(L/K)$, and generalize some known results for $Po(L/mathbb{Q})$ to $Ost(L/K)$.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42229788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 3
An algorithm taking Kirby diagrams to trisection diagrams 一种将柯比图转换为三分图的算法
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-10-31 DOI: 10.2140/pjm.2022.318.109
Willi Kepplinger
{"title":"An algorithm taking Kirby diagrams to trisection diagrams","authors":"Willi Kepplinger","doi":"10.2140/pjm.2022.318.109","DOIUrl":"https://doi.org/10.2140/pjm.2022.318.109","url":null,"abstract":"We present an algorithm taking a Kirby diagram of a closed oriented $4$-manifold to a trisection diagram of the same manifold. This algorithm provides us with a large number of examples for trisection diagrams of closed oriented $4$-manifolds since many Kirby-diagrammatic descriptions of closed oriented $4$-manifolds are known. That being said, the algorithm does not necessarily provide particularly efficient trisection diagrams. We also extend this algorithm to work for the non-orientable case.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41735235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 4
Orders of the canonical vector bundles over configuration spaces of finite graphs 有限图构型空间上正则向量束的阶数
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-10-25 DOI: 10.2140/pjm.2022.316.53
F. Cohen, R. Huang
{"title":"Orders of the canonical vector bundles over configuration spaces of finite graphs","authors":"F. Cohen, R. Huang","doi":"10.2140/pjm.2022.316.53","DOIUrl":"https://doi.org/10.2140/pjm.2022.316.53","url":null,"abstract":"We prove that the order of the canonical vector bundle over the configuration space is 2 for a general planar graph, and is 4 for a nonplanar graph.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45340324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On the global weak solution problem of semilinear generalized Tricomi equations, II 半线性广义Tricomi方程的整体弱解问题，2
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-10-15 DOI: 10.2140/pjm.2021.314.29
Daoyin He, I. Witt, Huicheng Yin
{"title":"On the global weak solution problem of semilinear generalized Tricomi equations, II","authors":"Daoyin He, I. Witt, Huicheng Yin","doi":"10.2140/pjm.2021.314.29","DOIUrl":"https://doi.org/10.2140/pjm.2021.314.29","url":null,"abstract":"","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47740877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On totally umbilical surfaces in the warpedproduct 𝕄(κ)f× I 在弯曲产物𝕄(κ) fxi的完全脐带表面
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-10-12 DOI: 10.2140/pjm.2021.313.343
Ady Cambraia Jr., Abigail Folha, C. Peñafiel
{"title":"On totally umbilical surfaces in the warped\u0000product 𝕄(κ)f× I","authors":"Ady Cambraia Jr., Abigail Folha, C. Peñafiel","doi":"10.2140/pjm.2021.313.343","DOIUrl":"https://doi.org/10.2140/pjm.2021.313.343","url":null,"abstract":"","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45485106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Isoperimetric bounds for lower-order eigenvalues 低阶特征值的等周界
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-10-05 DOI: 10.2140/pjm.2022.317.297
F. Fang, C. Xia
{"title":"Isoperimetric bounds for lower-order eigenvalues","authors":"F. Fang, C. Xia","doi":"10.2140/pjm.2022.317.297","DOIUrl":"https://doi.org/10.2140/pjm.2022.317.297","url":null,"abstract":"We adopt the convention that each eigenvalue is repeated according to its multiplicity. An important issue in spectral geometry is to obtain good estimates for these and other eigenvalues in terms of the geometric data of the manifold M such as the volume, the diameter, the curvature, the isoperimetric constants, etc. See [1],[2],[10],[13],[31] for references. On the other hand, after the seminal works of Bleecker-Weiner [4] and Reilly [30], the following approach is developed: the manifold (M, g) is immersed isometrically into another Riemannian manifold. One then gets good estimates for λk(M), mostly for λ1(M), in termos of the extrinsic geometric quantities of M . See for example [4], [15], [16], [23], [24], [35], [37]. Especially relevant for us is the quoted work of Reilly [30], where he obtained the following remarkable isoperimetric inequality for the first positive eigenvalue λ1(M) in the case that M is embedded as a hypersurface bounding a domain Ω in R: λ1(M) ≤ n− 1 n2 · |M | 2 |Ω|2 . (1.1)","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44643070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Representations of orientifoldKhovanov–Lauda–Rouquier algebras and the Enomoto–Kashiwara algebra OrientalifoldKhovanov–Lauda–Rouquier代数和Enomoto–Kashiwara代数的表示
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-10-04 DOI: 10.2140/pjm.2023.322.407
T. Przeździecki
{"title":"Representations of orientifold\u0000Khovanov–Lauda–Rouquier algebras and the Enomoto–Kashiwara algebra","authors":"T. Przeździecki","doi":"10.2140/pjm.2023.322.407","DOIUrl":"https://doi.org/10.2140/pjm.2023.322.407","url":null,"abstract":"We consider an\"orientifold\"generalization of Khovanov-Lauda-Rouquier algebras, depending on a quiver with an involution and a framing. Their representation theory is related, via a Schur-Weyl duality type functor, to Kac-Moody quantum symmetric pairs, and, via a categorification theorem, to highest weight modules over an algebra introduced by Enomoto and Kashiwara. Our first main result is a new shuffle realization of these highest weight modules and a combinatorial construction of their PBW and canonical bases in terms of Lyndon words. Our second main result is a classification of irreducible representations of orientifold KLR algebras and a computation of their global dimension in the case when the framing is trivial.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43299820","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 2
A note on the two-dimensional Lagrangian mean curvature equation 关于二维拉格朗日平均曲率方程的注解
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-10-04 DOI: 10.2140/pjm.2022.318.43
A. Bhattacharya
{"title":"A note on the two-dimensional Lagrangian mean curvature equation","authors":"A. Bhattacharya","doi":"10.2140/pjm.2022.318.43","DOIUrl":"https://doi.org/10.2140/pjm.2022.318.43","url":null,"abstract":"In this note, we use Warren-Yuan's super isoperimetric inequality on the level sets of subharmonic functions, which is available only in two dimensions, to derive a modified Hessian bound for solutions of the two dimensional Lagrangian mean curvature equation. We assume the Lagrangian phase to be supercritical with bounded second derivatives. Unlike the previous approach, the simplified approach in this proof does not require the Michael-Simon mean value and Sobolev inequalities on generalized submanifolds of $mathbb{R}^n$.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48851459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 3
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