Pub Date : 2023-01-01DOI: 10.4310/arkiv.2023.v61.n1.a1
S. Baek, N. Karpenko
{"title":"Yagita’s counter-examples and beyond","authors":"S. Baek, N. Karpenko","doi":"10.4310/arkiv.2023.v61.n1.a1","DOIUrl":"https://doi.org/10.4310/arkiv.2023.v61.n1.a1","url":null,"abstract":"","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70393975","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 : 2023-01-01DOI: 10.4310/arkiv.2023.v61.n2.a3
Alessio Cela
We compute the quantum Euler class of Fano complete intersections X in a projective space. In particular, we prove a recent conjecture of A. Buch and R. Pandharipande. Finally we apply our result to obtain formulas for the virtual Tevelev degrees of X. An algorithm computing all genus 0 two-point Hyperplane Gromov Witten invariants of X is illustrated along the way.
{"title":"Quantum Euler class and virtual Tevelev degrees of Fano complete intersections","authors":"Alessio Cela","doi":"10.4310/arkiv.2023.v61.n2.a3","DOIUrl":"https://doi.org/10.4310/arkiv.2023.v61.n2.a3","url":null,"abstract":"We compute the quantum Euler class of Fano complete intersections X in a projective space. In particular, we prove a recent conjecture of A. Buch and R. Pandharipande. Finally we apply our result to obtain formulas for the virtual Tevelev degrees of X. An algorithm computing all genus 0 two-point Hyperplane Gromov Witten invariants of X is illustrated along the way.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135660382","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 : 2022-05-12DOI: 10.4310/arkiv.2023.v61.n1.a2
F. Bayart
We give sufficient conditions for a general Dirichlet series to be universal with respect to translations or rearrangements.
我们给出了一般狄利克雷级数对于平移或重排是普遍的充分条件。
{"title":"Universality of general Dirichlet series with respect to translations and rearrangements","authors":"F. Bayart","doi":"10.4310/arkiv.2023.v61.n1.a2","DOIUrl":"https://doi.org/10.4310/arkiv.2023.v61.n1.a2","url":null,"abstract":"We give sufficient conditions for a general Dirichlet series to be universal with respect to translations or rearrangements.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70394516","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 : 2022-03-27DOI: 10.4310/arkiv.2023.v61.n1.a7
Yang Li, Jun Zhao, Yuanyuan Zhang, Genqiang Liu
For any $nin mathbb{Z}_{geq 2}$, let $mathfrak{m}_n$ be the subalgebra of $mathfrak{sp}_{2n}$ spanned by all long negative root vectors $X_{-2epsilon_i}$, $i=1,dots,n$. An $mathfrak{sp}_{2n}$-module $M$ is called a Whittaker module with respect to the Whittaker pair $(mathfrak{sp}_{2n},mathfrak{m}_n)$ if the action of $mathfrak{m}_n$ on $M$ is locally finite, according to a definition of Batra and Mazorchuk. This kind of modules are more general than the classical Whittaker modules defined by Kostant. In this paper, we show that each non-singular block $mathcal{WH}_{mathbf{a}}^{mu}$ with finite dimensional Whittaker vector subspaces is equivalent to a module category $mathcal{W}^{mathbf{a}}$ of the even Weyl algebra $mathcal{D}_n^{ev}$ which is semi-simple. As a corollary, any simple module in the block $mathcal{WH}_{mathbf{i}}^{-frac{1}{2}omega_n}$ for the fundamental weight $omega_n$ is equivalent to the Nilsson's module $N_{mathbf{i}}$ up to an automorphism of $mathfrak{sp}_{2n}$. We also characterize all possible algebra homomorphisms from $U(mathfrak{sp}_{2n})$ to the Weyl algebra $mathcal{D}_n$ under a natural condition.
{"title":"A Whittaker category for the symplectic Lie algebra and differential operators","authors":"Yang Li, Jun Zhao, Yuanyuan Zhang, Genqiang Liu","doi":"10.4310/arkiv.2023.v61.n1.a7","DOIUrl":"https://doi.org/10.4310/arkiv.2023.v61.n1.a7","url":null,"abstract":"For any $nin mathbb{Z}_{geq 2}$, let $mathfrak{m}_n$ be the subalgebra of $mathfrak{sp}_{2n}$ spanned by all long negative root vectors $X_{-2epsilon_i}$, $i=1,dots,n$. An $mathfrak{sp}_{2n}$-module $M$ is called a Whittaker module with respect to the Whittaker pair $(mathfrak{sp}_{2n},mathfrak{m}_n)$ if the action of $mathfrak{m}_n$ on $M$ is locally finite, according to a definition of Batra and Mazorchuk. This kind of modules are more general than the classical Whittaker modules defined by Kostant. In this paper, we show that each non-singular block $mathcal{WH}_{mathbf{a}}^{mu}$ with finite dimensional Whittaker vector subspaces is equivalent to a module category $mathcal{W}^{mathbf{a}}$ of the even Weyl algebra $mathcal{D}_n^{ev}$ which is semi-simple. As a corollary, any simple module in the block $mathcal{WH}_{mathbf{i}}^{-frac{1}{2}omega_n}$ for the fundamental weight $omega_n$ is equivalent to the Nilsson's module $N_{mathbf{i}}$ up to an automorphism of $mathfrak{sp}_{2n}$. We also characterize all possible algebra homomorphisms from $U(mathfrak{sp}_{2n})$ to the Weyl algebra $mathcal{D}_n$ under a natural condition.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70394607","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 : 2022-03-24DOI: 10.4310/arkiv.2022.v60.n2.a9
L. Hitruhin
. We improve both dimension compression and expansion bounds for homeomorphisms with p -exponentially integrable distortion. To the first direction we also introduce estimates for the compression multifractal spectra, which will be used to estimate compression of dimension, and for the rotational multifractal spectra. For establishing the expansion case we use the multifractal spectra of the inverse mapping and construct examples proving sharpness.
{"title":"Dimension compression and expansion under homeomorphisms with exponentially integrable distortion","authors":"L. Hitruhin","doi":"10.4310/arkiv.2022.v60.n2.a9","DOIUrl":"https://doi.org/10.4310/arkiv.2022.v60.n2.a9","url":null,"abstract":". We improve both dimension compression and expansion bounds for homeomorphisms with p -exponentially integrable distortion. To the first direction we also introduce estimates for the compression multifractal spectra, which will be used to estimate compression of dimension, and for the rotational multifractal spectra. For establishing the expansion case we use the multifractal spectra of the inverse mapping and construct examples proving sharpness.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47511940","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 : 2022-01-01DOI: 10.4310/arkiv.2022.v60.n2.a2
Odysseas N. Bakas, S. Pott, Salvador Rodríguez-López, A. Sola
{"title":"Notes on $H^{log}$: structural properties, dyadic variants, and bilinear $H^1$-$operatorname{BMO}$ mappings","authors":"Odysseas N. Bakas, S. Pott, Salvador Rodríguez-López, A. Sola","doi":"10.4310/arkiv.2022.v60.n2.a2","DOIUrl":"https://doi.org/10.4310/arkiv.2022.v60.n2.a2","url":null,"abstract":"","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70393530","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 : 2022-01-01DOI: 10.4310/arkiv.2022.v60.n2.a4
A. Campillo, F. Delgado, S. Gusein-Zade
{"title":"Weil–Poincaré series and topology of collections of valuations on rational double points","authors":"A. Campillo, F. Delgado, S. Gusein-Zade","doi":"10.4310/arkiv.2022.v60.n2.a4","DOIUrl":"https://doi.org/10.4310/arkiv.2022.v60.n2.a4","url":null,"abstract":"","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70394113","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 : 2022-01-01DOI: 10.4310/arkiv.2022.v60.n1.a9
V. Totik
. A conjecture of T. Richards is proven which yields a quantitative version of the classical Gauss-Lucas theorem: if K is a convex set, then for every ε> 0 there is an α ε < 1 such that if a polynomial P n of degree at most n has k ≥ α ε n zeros in K , then P (cid:2) n has at least k − 1 zeros in the ε -neighborhood of K . Estimates are given for the dependence of α ε on ε .
{"title":"A quantitative Gauss–Lucas theorem","authors":"V. Totik","doi":"10.4310/arkiv.2022.v60.n1.a9","DOIUrl":"https://doi.org/10.4310/arkiv.2022.v60.n1.a9","url":null,"abstract":". A conjecture of T. Richards is proven which yields a quantitative version of the classical Gauss-Lucas theorem: if K is a convex set, then for every ε> 0 there is an α ε < 1 such that if a polynomial P n of degree at most n has k ≥ α ε n zeros in K , then P (cid:2) n has at least k − 1 zeros in the ε -neighborhood of K . Estimates are given for the dependence of α ε on ε .","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70393460","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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