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Multplicities and degree relative to a set 相对于集合的多重性和程度
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE Pub Date : 2022-10-03 DOI: 10.2422/2036-2145.202111_004
V. Grandjean
{"title":"Multplicities and degree relative to a set","authors":"V. Grandjean","doi":"10.2422/2036-2145.202111_004","DOIUrl":"https://doi.org/10.2422/2036-2145.202111_004","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"77 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85914628","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}
引用次数: 0
Stability of the vortex in micromagnetics and related models 微磁学中涡旋的稳定性及相关模型
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE Pub Date : 2022-09-16 DOI: 10.2422/2036-2145.202209_012
X. Lamy, E. Marconi
{"title":"Stability of the vortex in micromagnetics and related models","authors":"X. Lamy, E. Marconi","doi":"10.2422/2036-2145.202209_012","DOIUrl":"https://doi.org/10.2422/2036-2145.202209_012","url":null,"abstract":"We consider line-energy models of Ginzburg-Landau type in a two-dimensional simply-connected bounded domain. Configurations of vanishing energy have been characterized by Jabin, Otto and Perthame: the domain must be a disk, and the configuration a vortex. We prove a quantitative version of this statement in the class of $C^{1,1}$ domains, improving on previous results by Lorent. In particular, the deviation of the domain from a disk is controlled by a power of the energy, and that power is optimal. The main tool is a Lagrangian representation introduced by the second author, which allows to decompose the energy along characteristic curves.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"82 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83970088","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}
引用次数: 2
Rational blowdown graphs for symplectic fillings of lens spaces 透镜空间辛填充的有理排污图
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE Pub Date : 2022-09-07 DOI: 10.2422/2036-2145.202209_004
M. Bhupal, B. Ozbagci
{"title":"Rational blowdown graphs for symplectic fillings of lens spaces","authors":"M. Bhupal, B. Ozbagci","doi":"10.2422/2036-2145.202209_004","DOIUrl":"https://doi.org/10.2422/2036-2145.202209_004","url":null,"abstract":"In a previous work, we proved that each minimal symplectic filling of any oriented lens space, viewed as the singularity link of some cyclic quotient singularity and equipped with its canonical contact structure, can be obtained from the minimal resolution of the singularity by a sequence of symplectic rational blowdowns along linear plumbing graphs. Here we give a dramatically simpler visual presentation of our rational blowdown algorithm in terms of the triangulations of a convex polygon. As a consequence, we are able to organize the symplectic deformation equivalence classes of all minimal symplectic fillings of any given lens space equipped with its canonical contact structure, as a graded, directed, rooted, and connected graph, where the root is the minimal resolution of the corresponding cyclic quotient singularity and each directed edge is a symplectic rational blowdown along an explicit linear plumbing graph. Moreover, we provide an upper bound for the rational blowdown depth of each minimal symplectic filling.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85415751","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}
引用次数: 0
Loewner PDE, inverse Loewner chains and nonlinear resolvents of the Carathéodory family in infinite dimensions Loewner偏微分方程，逆Loewner链和无限维carath<s:1>一族的非线性解
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE Pub Date : 2022-07-28 DOI: 10.2422/2036-2145.202107_004
H. Hamada, G. Kohr
{"title":"Loewner PDE, inverse Loewner chains and nonlinear resolvents of the Carathéodory family in infinite dimensions","authors":"H. Hamada, G. Kohr","doi":"10.2422/2036-2145.202107_004","DOIUrl":"https://doi.org/10.2422/2036-2145.202107_004","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80589048","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}
引用次数: 1
On the quantitative isoperimetric inequality in the plane with the barycentric asymmetry 质心不对称平面上的定量等周不等式
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE Pub Date : 2022-07-28 DOI: 10.2422/2036-2145.202202_011
Alexandre Arias Junior, A. Ascanelli, M. Cappiello
{"title":"On the quantitative isoperimetric inequality in the plane with the barycentric asymmetry","authors":"Alexandre Arias Junior, A. Ascanelli, M. Cappiello","doi":"10.2422/2036-2145.202202_011","DOIUrl":"https://doi.org/10.2422/2036-2145.202202_011","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86975868","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}
引用次数: 5
Slope inequalities for higher dimensional irregular fibrations 高维不规则振动的斜率不等式
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE Pub Date : 2022-07-28 DOI: 10.2422/2036-2145.202109_012
M. A. Barja
{"title":"Slope inequalities for higher dimensional irregular fibrations","authors":"M. A. Barja","doi":"10.2422/2036-2145.202109_012","DOIUrl":"https://doi.org/10.2422/2036-2145.202109_012","url":null,"abstract":"We prove the equivalence between Clifford-Severi inequalities for good classes of varieties of maximal Albanese dimension and Slope Inequalities for such varieties fibred over curves. This provides a big set of new Slope Inequalities and characterizes the limit cases. It also gives a machinery to automatically obtain other higher dimensional Slope and CliffordSeveri inequalities from inequalities in low dimension. For this, we construct a continuous version of Xiao’s method for irregular fibrations.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73899770","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}
引用次数: 2
Harmonic flow of Spin(7)-structures 自旋(7)结构的谐波流
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE Pub Date : 2022-07-28 DOI: 10.2422/2036-2145.202111_026
S. Dwivedi, E. Loubeau, Henrique N. Sá Earp
{"title":"Harmonic flow of Spin(7)-structures","authors":"S. Dwivedi, E. Loubeau, Henrique N. Sá Earp","doi":"10.2422/2036-2145.202111_026","DOIUrl":"https://doi.org/10.2422/2036-2145.202111_026","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"207 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73004535","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}
引用次数: 3
The rational Chow rings of moduli spaces of hyperelliptic curves with marked points 带标记点的超椭圆曲线模空间的有理Chow环
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE Pub Date : 2022-07-22 DOI: 10.2422/2036-2145.202208_012
Samir Canning, H. Larson
{"title":"The rational Chow rings of moduli spaces of hyperelliptic curves with marked points","authors":"Samir Canning, H. Larson","doi":"10.2422/2036-2145.202208_012","DOIUrl":"https://doi.org/10.2422/2036-2145.202208_012","url":null,"abstract":"We determine the rational Chow ring of the moduli space $mathcal{H}_{g,n}$ of $n$-pointed smooth hyperelliptic curves of genus $g$ when $n leq 2g+6$. We also show that the Chow ring of the partial compactification $mathcal{I}_{g,n}$, parametrizing $n$-pointed irreducible nodal hyperelliptic curves, is generated by tautological divisors. Along the way, we improve Casnati's result that $mathcal{H}_{g,n}$ is rational for $n leq 2g+8$ to show $mathcal{H}_{g,n}$ is rational for $n leq 3g+5$.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85008495","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}
引用次数: 3
Existence of nonsymmetric logarithmic spiral vortex sheet solutions to the 2D Euler equations 二维欧拉方程非对称对数螺旋涡片解的存在性
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE Pub Date : 2022-07-13 DOI: 10.2422/2036-2145.202208_003
T. Cie'slak, P. Kokocki, W. O.za'nski
{"title":"Existence of nonsymmetric logarithmic spiral vortex sheet solutions to the 2D Euler equations","authors":"T. Cie'slak, P. Kokocki, W. O.za'nski","doi":"10.2422/2036-2145.202208_003","DOIUrl":"https://doi.org/10.2422/2036-2145.202208_003","url":null,"abstract":"We consider solutions of the 2D incompressible Euler equation in the form of $Mgeq 1$ cocentric logarithmic spirals. We prove the existence of a generic family of spirals that are nonsymmetric in the sense that the angles of the individual spirals are not uniformly distributed over the unit circle. Namely, we show that if $M=2$ or $Mgeq 3 $ is an odd integer such that certain non-degeneracy conditions hold, then, for each $n in { 1,2 }$, there exists a logarithmic spiral with $M$ branches of relative angles arbitrarily close to $bartheta_{k} = knpi/M$ for $k=0,1,ldots , M-1$, which include halves of the angles of the Alexander spirals. We show that the non-degeneracy conditions are satisfied if $Min { 2, 3,5,7,9 }$, and that the conditions hold for all odd $M>9$ given a certain gradient matrix is invertible, which appears to be true by numerical computations.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82502245","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}
引用次数: 8
Covering numbers for characters of symmetric groups 涵盖对称群字符的数字
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE Pub Date : 2022-06-19 DOI: 10.2422/2036-2145.202302_003
A. Miller
{"title":"Covering numbers for characters of symmetric groups","authors":"A. Miller","doi":"10.2422/2036-2145.202302_003","DOIUrl":"https://doi.org/10.2422/2036-2145.202302_003","url":null,"abstract":"If $n>4$ and $c(theta)$ denotes the set of irreducible constituents of a character $theta$, then $c(chi^k)={rm Irr}(S_n)$ for all nonlinear $chiin {rm Irr}(S_n)$ if and only if $kgeq n-1$.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89441414","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}
引用次数: 0
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