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On fields of meromorphic functions on neighborhoods of rational curves 论有理曲线邻域上的分形函数场
arXiv - MATH - Complex Variables Pub Date : 2024-08-26 DOI: arxiv-2408.14061
Serge Lvovski
{"title":"On fields of meromorphic functions on neighborhoods of rational curves","authors":"Serge Lvovski","doi":"arxiv-2408.14061","DOIUrl":"https://doi.org/arxiv-2408.14061","url":null,"abstract":"Suppose that $F$ is a smooth and connected complex surface (not necessarily\u0000compact) containing a smooth rational curve with positive self-intersection. We\u0000prove that if there exists a non-constant meromorphic function on $F$, then the\u0000field of meromorphic functions on $F$ is isomorphic to the field of rational\u0000functions in one or two variables over $mathbb C$.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201857","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
Local algebraicity and localization of the Bergman kernel on Stein spaces with finite type boundaries 具有有限类型边界的斯坦因空间上伯格曼核的局部代数性和局部化
arXiv - MATH - Complex Variables Pub Date : 2024-08-26 DOI: arxiv-2408.13989
Peter Ebenfelt, Soumya Ganguly, Ming Xiao
{"title":"Local algebraicity and localization of the Bergman kernel on Stein spaces with finite type boundaries","authors":"Peter Ebenfelt, Soumya Ganguly, Ming Xiao","doi":"arxiv-2408.13989","DOIUrl":"https://doi.org/arxiv-2408.13989","url":null,"abstract":"On a two dimensional Stein space with isolated, normal singularities, smooth\u0000finite type boundary, and locally algebraic Bergman kernel, we establish an\u0000estimate on the type of the boundary in terms of the local algebraic degree of\u0000the Bergman kernel. As an application, we characterize two dimensional ball\u0000quotients as the only Stein spaces with smooth finite type boundary and locally\u0000rational Bergman kernel. A key ingredient in the proof of the degree estimate\u0000is a new localization result for the Bergman kernel of a pseudoconvex, finite\u0000type domain in a complex manifold.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201867","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
Picard-Fuchs system for family of Kummer surfaces as subsystem of GKZ hypregeometric system 作为 GKZ 次几何系统子系统的库默曲面族皮卡-福克斯系统
arXiv - MATH - Complex Variables Pub Date : 2024-08-26 DOI: arxiv-2408.14271
Atsuhira Nagano
{"title":"Picard-Fuchs system for family of Kummer surfaces as subsystem of GKZ hypregeometric system","authors":"Atsuhira Nagano","doi":"arxiv-2408.14271","DOIUrl":"https://doi.org/arxiv-2408.14271","url":null,"abstract":"We determine a simple expression of the Picard-Fuchs system for a family of\u0000Kummer surfaces for all principally polarized Abelian surfaces. It is given by\u0000a system of linear partial differential equations in three variables of rank\u0000five. Our results are based on a Jacobian elliptic fibration on Kummer surfaces\u0000and a GKZ hypergeometric system suited to the elliptic fibration.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"400 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201864","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
Weighted norm inequalities of various square functions and Volterra integral operators on the unit ball 单位球上各种平方函数和 Volterra 积分算子的加权规范不等式
arXiv - MATH - Complex Variables Pub Date : 2024-08-25 DOI: arxiv-2408.13726
Changbao Pang, Maofa Wang, Bang Xu, Hao Zhang
{"title":"Weighted norm inequalities of various square functions and Volterra integral operators on the unit ball","authors":"Changbao Pang, Maofa Wang, Bang Xu, Hao Zhang","doi":"arxiv-2408.13726","DOIUrl":"https://doi.org/arxiv-2408.13726","url":null,"abstract":"In this paper, we investigate various square functions on the unit complex\u0000ball. We prove the weighted inequalities of the Lusin area integral associated\u0000with Poisson integral in terms of $A_p$ weights for all $1<p<infty$; this\u0000gives an affirmative answer to an open question raised by Segovia and Wheeden.\u0000To that end, we establish the weighted inequalities for Littlewood-Paley type\u0000square functions. As an interesting application, we obtain the weighted\u0000inequalities of the Lusin area integral associated with Bergman gradient. In\u0000addition, we get an equivalent characterization of weighted Hardy spaces by\u0000means of the Lusin area integral in the context of holomorphic functions. We\u0000also obtain the weighted inequalities for Volterra integral operators. The key\u0000ingredients of our proof involve complex analysis, Calder'on-Zygmund theory,\u0000the local mean oscillation technique and sparse domination.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142225826","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
Properties and applications of the Bicomplex Miller-Ross function 双复米勒-罗斯函数的性质和应用
arXiv - MATH - Complex Variables Pub Date : 2024-08-23 DOI: arxiv-2408.13246
Snehasis Bera, Sourav Das, Abhijit Banerjee
{"title":"Properties and applications of the Bicomplex Miller-Ross function","authors":"Snehasis Bera, Sourav Das, Abhijit Banerjee","doi":"arxiv-2408.13246","DOIUrl":"https://doi.org/arxiv-2408.13246","url":null,"abstract":"In this work, Miller Ross function with bicomplex arguments has been\u0000introduced. Various properties of this function including recurrence relations,\u0000integral representations and differential relations are established.\u0000Furthermore, the bicomplex holomorphicity and Taylor series representation of\u0000this function are discussed, along with the derivation of a differential\u0000equation. Finally, as applications some relations of fractional order\u0000derivatives and solutions for the bicomplex extension of the generalized\u0000fractional kinetic equation involving the bicomplex Miller Ross function are\u0000derived.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201861","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
A residue formula for integrals with hyperplane singularities 有超平面奇点的积分的残差公式
arXiv - MATH - Complex Variables Pub Date : 2024-08-22 DOI: arxiv-2408.12586
Andrew O'Desky
{"title":"A residue formula for integrals with hyperplane singularities","authors":"Andrew O'Desky","doi":"arxiv-2408.12586","DOIUrl":"https://doi.org/arxiv-2408.12586","url":null,"abstract":"We prove a new residue formula for integrals with singularities along affine\u0000hyperplanes. Our formula makes use of a notion for real matrices called\u0000stability which is inspired by ideas from total positivity.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"16 3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201863","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
On parametric $0$-Gevrey asymptotic expansions in two levels for some linear partial $q$-difference-differential equations 关于某些线性偏 $q$-差分-微分方程的参数 $0$-Gevrey 两级渐近展开
arXiv - MATH - Complex Variables Pub Date : 2024-08-22 DOI: arxiv-2408.12335
Alberto Lastra, Stephane Malek
{"title":"On parametric $0$-Gevrey asymptotic expansions in two levels for some linear partial $q$-difference-differential equations","authors":"Alberto Lastra, Stephane Malek","doi":"arxiv-2408.12335","DOIUrl":"https://doi.org/arxiv-2408.12335","url":null,"abstract":"A novel asymptotic representation of the analytic solutions to a family of\u0000singularly perturbed $q-$difference-differential equations in the complex\u0000domain is obtained. Such asymptotic relation shows two different levels\u0000associated to the vanishing rate of the domains of the coefficients in the\u0000formal asymptotic expansion. On the way, a novel version of a multilevel\u0000sequential Ramis-Sibuya type theorem is achieved.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201862","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
On reflection maps from n-space to n+1-space 关于从 n 空间到 n+1 空间的反射映射
arXiv - MATH - Complex Variables Pub Date : 2024-08-21 DOI: arxiv-2408.11669
Milena Barbosa Gama, Otoniel Nogueira da Silva
{"title":"On reflection maps from n-space to n+1-space","authors":"Milena Barbosa Gama, Otoniel Nogueira da Silva","doi":"arxiv-2408.11669","DOIUrl":"https://doi.org/arxiv-2408.11669","url":null,"abstract":"In this work we consider some problems about a reflected graph map germ $f$\u0000from $(mathbb{C}^n,0)$ to $(mathbb{C}^{n+1},0)$. A reflected graph map is a\u0000particular case of a reflection map, which is defined using an embedding of\u0000$mathbb{C}^n$ in $mathbb{C}^{p}$ and then applying the action of a reflection\u0000group $G$ on $mathbb{C}^{p}$. In this work, we present a description of the\u0000presentation matrix of $f_*{cal O}_n$ as an ${cal O}_{n+1}$-module via $f$ in\u0000terms of the action of the associated reflection group $G$. We also give a\u0000description for a defining equation of the image of $f$ in terms of the action\u0000of $G$. Finally, we present an upper (and also a lower) bound for the\u0000multiplicity of the image of $f$ and some applications.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201865","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
On a Mattei-Salem theorem 关于马泰-萨利姆定理
arXiv - MATH - Complex Variables Pub Date : 2024-08-20 DOI: arxiv-2408.10767
Arturo Fernández-Pérez, Nancy Saravia-Molina
{"title":"On a Mattei-Salem theorem","authors":"Arturo Fernández-Pérez, Nancy Saravia-Molina","doi":"arxiv-2408.10767","DOIUrl":"https://doi.org/arxiv-2408.10767","url":null,"abstract":"We investigate the relationship between the valuations of a germ of a\u0000singular foliation $mathcal{F}$ on the complex plane and those of a balanced\u0000equation of separatrices for $mathcal{F}$, extending a theorem by\u0000Mattei-Salem. Under certain conditions, we also derive inequalities involving\u0000the valuation, tangency excess, and degree of a holomorphic foliation\u0000$mathcal{F}$ on the complex projective plane.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201866","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
On holomorphic $mathbb{C}^*$-actions 关于全态 $mathbb{C}^*$ 作用
arXiv - MATH - Complex Variables Pub Date : 2024-08-19 DOI: arxiv-2408.09625
Víctor León, Bruno Scárdua
{"title":"On holomorphic $mathbb{C}^*$-actions","authors":"Víctor León, Bruno Scárdua","doi":"arxiv-2408.09625","DOIUrl":"https://doi.org/arxiv-2408.09625","url":null,"abstract":"In this paper we study holomorphic actions of the complex multiplicative\u0000group on complex manifolds around a singular (fixed) point. We prove\u0000linearization results for the germ of action and also for the whole action\u0000under some conditions on the manifold. This can be seen as a follow-up to\u0000previous works of M. Suzuki and other authors.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201868","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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