Pub Date : 2023-07-25DOI: 10.1017/S0017089523000174
Abel Castorena, Juan Bosco Fr'ias-Medina
Abstract In this work, we study the Humbert-Edge curves of type 5, defined as a complete intersection of four diagonal quadrics in ${mathbb{P}}^5$ . We characterize them using Kummer surfaces, and using the geometry of these surfaces, we construct some vanishing thetanulls on such curves. In addition, we describe an argument to give an isomorphism between the moduli space of Humbert-Edge curves of type 5 and the moduli space of hyperelliptic curves of genus 2, and we show how this argument can be generalized to state an isomorphism between the moduli space of hyperelliptic curves of genus $g=frac{n-1}{2}$ and the moduli space of Humbert-Edge curves of type $ngeq 5$ where $n$ is an odd number.
{"title":"Geometric aspects on Humbert-Edge curves of type 5, Kummer surfaces and hyperelliptic curves of genus 2","authors":"Abel Castorena, Juan Bosco Fr'ias-Medina","doi":"10.1017/S0017089523000174","DOIUrl":"https://doi.org/10.1017/S0017089523000174","url":null,"abstract":"Abstract In this work, we study the Humbert-Edge curves of type 5, defined as a complete intersection of four diagonal quadrics in \u0000${mathbb{P}}^5$\u0000 . We characterize them using Kummer surfaces, and using the geometry of these surfaces, we construct some vanishing thetanulls on such curves. In addition, we describe an argument to give an isomorphism between the moduli space of Humbert-Edge curves of type 5 and the moduli space of hyperelliptic curves of genus 2, and we show how this argument can be generalized to state an isomorphism between the moduli space of hyperelliptic curves of genus \u0000$g=frac{n-1}{2}$\u0000 and the moduli space of Humbert-Edge curves of type \u0000$ngeq 5$\u0000 where \u0000$n$\u0000 is an odd number.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48671226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-25DOI: 10.1017/S0017089523000186
Jieyan Wang, Baohua Xie
Abstract A. Mark and J. Paupert [Presentations for cusped arithmetic hyperbolic lattices, 2018, arXiv:1709.06691.] presented a method to compute a presentation for any cusped complex hyperbolic lattice. In this note, we will use their method to give a presentation for the Eisenstein-Picard modular group in three complex dimensions.
{"title":"A presentation for the Eisenstein-Picard modular group in three complex dimensions","authors":"Jieyan Wang, Baohua Xie","doi":"10.1017/S0017089523000186","DOIUrl":"https://doi.org/10.1017/S0017089523000186","url":null,"abstract":"Abstract A. Mark and J. Paupert [Presentations for cusped arithmetic hyperbolic lattices, 2018, arXiv:1709.06691.] presented a method to compute a presentation for any cusped complex hyperbolic lattice. In this note, we will use their method to give a presentation for the Eisenstein-Picard modular group in three complex dimensions.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42063740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-10DOI: 10.1017/S0017089523000162
Xi Tang
Abstract This paper is devoted to the study of generalized tilting theory of functor categories in different levels. First, we extend Miyashita’s proof (Math Z 193:113–146,1986) of the generalized Brenner–Butler theorem to arbitrary functor categories $mathop{textrm{Mod}}nolimits!(mathcal{C})$ with $mathcal{C}$ an annuli variety. Second, a hereditary and complete cotorsion pair generated by a generalized tilting subcategory $mathcal{T}$ of $mathop{textrm{Mod}}nolimits !(mathcal{C})$ is constructed. Some applications of these two results include the equivalence of Grothendieck groups $K_0(mathcal{C})$ and $K_0(mathcal{T})$ , the existences of a new abelian model structure on the category of complexes $mathop{textrm{C}}nolimits !(!mathop{textrm{Mod}}nolimits!(mathcal{C}))$ , and a t-structure on the derived category $mathop{textrm{D}}nolimits !(!mathop{textrm{Mod}}nolimits !(mathcal{C}))$ .
本文致力于在不同层次上研究函子范畴的广义倾斜理论。首先，我们将广义Brenner–Butler定理的Miyashita证明（Math Z 193:113–1461986）推广到任意函子范畴$mathop｛textrm｛Mod｝｝nolimits！（mathcal｛C｝）$与$mathcal{C｝$是环状变体。其次，由$mathop｛textrm｛Mod｝｝nolimits的广义倾斜子类别$mathcal｛T｝$生成的一个遗传完全余子对！构造了（mathcal｛C｝）$。这两个结果的一些应用包括Grothendieck群$K_0（mathcal｛C｝）$和$K_0！（！mathop｛textrm｛Mod｝｝nolimits！（！mathop｛textrm｛Mod｝｝nolimits！（mathcal｛C｝））$。
{"title":"Generalized tilting theory in functor categories","authors":"Xi Tang","doi":"10.1017/S0017089523000162","DOIUrl":"https://doi.org/10.1017/S0017089523000162","url":null,"abstract":"Abstract This paper is devoted to the study of generalized tilting theory of functor categories in different levels. First, we extend Miyashita’s proof (Math Z 193:113–146,1986) of the generalized Brenner–Butler theorem to arbitrary functor categories \u0000$mathop{textrm{Mod}}nolimits!(mathcal{C})$\u0000 with \u0000$mathcal{C}$\u0000 an annuli variety. Second, a hereditary and complete cotorsion pair generated by a generalized tilting subcategory \u0000$mathcal{T}$\u0000 of \u0000$mathop{textrm{Mod}}nolimits !(mathcal{C})$\u0000 is constructed. Some applications of these two results include the equivalence of Grothendieck groups \u0000$K_0(mathcal{C})$\u0000 and \u0000$K_0(mathcal{T})$\u0000 , the existences of a new abelian model structure on the category of complexes \u0000$mathop{textrm{C}}nolimits !(!mathop{textrm{Mod}}nolimits!(mathcal{C}))$\u0000 , and a t-structure on the derived category \u0000$mathop{textrm{D}}nolimits !(!mathop{textrm{Mod}}nolimits !(mathcal{C}))$\u0000 .","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48800944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-13DOI: 10.1017/S0017089523000046
Q. Song
Abstract In this paper, we study the Hausdorff dimension of sets defined by almost convergent binary expansion sequences. More precisely, the Hausdorff dimension of the following set begin{align*} bigg{xin[0,1);:;frac{1}{n}sum_{k=a}^{a+n-1}x_{k}longrightarrowalphatextrm{ uniformly in }ainmathbb{N}textrm{ as }nrightarrowinftybigg} end{align*} is determined for any $ alphain[0,1] $ . This completes a question considered by Usachev [Glasg. Math. J. 64 (2022), 691–697] where only the dimension for rational $ alpha $ is given.
{"title":"Hausdorff dimension of sets defined by almost convergent binary expansion sequences","authors":"Q. Song","doi":"10.1017/S0017089523000046","DOIUrl":"https://doi.org/10.1017/S0017089523000046","url":null,"abstract":"Abstract In this paper, we study the Hausdorff dimension of sets defined by almost convergent binary expansion sequences. More precisely, the Hausdorff dimension of the following set \u0000begin{align*} bigg{xin[0,1);:;frac{1}{n}sum_{k=a}^{a+n-1}x_{k}longrightarrowalphatextrm{ uniformly in }ainmathbb{N}textrm{ as }nrightarrowinftybigg} end{align*}\u0000 is determined for any \u0000$ alphain[0,1] $\u0000 . This completes a question considered by Usachev [Glasg. Math. J. 64 (2022), 691–697] where only the dimension for rational \u0000$ alpha $\u0000 is given.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47513362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-13DOI: 10.1017/S0017089523000034
Márcio S. Santos
Abstract In this short note, we deal with complete noncompact expanding and steady Ricci solitons of dimension $ngeq 3.$ More precisely, under an integrability assumption, we obtain a characterization for the generalized cigar Ricci soliton and the Gaussian Ricci soliton.
{"title":"Some characterizations of expanding and steady Ricci solitons","authors":"Márcio S. Santos","doi":"10.1017/S0017089523000034","DOIUrl":"https://doi.org/10.1017/S0017089523000034","url":null,"abstract":"Abstract In this short note, we deal with complete noncompact expanding and steady Ricci solitons of dimension \u0000$ngeq 3.$\u0000 More precisely, under an integrability assumption, we obtain a characterization for the generalized cigar Ricci soliton and the Gaussian Ricci soliton.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44363017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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