Mathematische Nachrichten最新文献

{"title":"Mori dream bonds and \u0000 \u0000 \u0000 C\u0000 ∗\u0000 \u0000 ${mathbb {C}}^*$\u0000 -actions","authors":"Lorenzo Barban,&nbsp;Eleonora A. Romano,&nbsp;Luis E. Solá Conde,&nbsp;Stefano Urbinati","doi":"10.1002/mana.202300586","DOIUrl":"https://doi.org/10.1002/mana.202300586","url":null,"abstract":"<p>We construct a correspondence between Mori dream regions arising from small modifications of normal projective varieties and <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>${mathbb {C}}^*$</annotation>\u0000 </semantics></math>-actions on polarized pairs which are bordisms. Moreover, we show that the Mori dream regions constructed in this way admit a chamber decomposition on which the models are the geometric quotients of the <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>${mathbb {C}}^*$</annotation>\u0000 </semantics></math>-action. In addition, we construct, from a given <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>${mathbb {C}}^*$</annotation>\u0000 </semantics></math>-action on a polarized pair for which there exist at least two admissible geometric quotients, a <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>${mathbb {C}}^*$</annotation>\u0000 </semantics></math>-equivariantly birational <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>${mathbb {C}}^*$</annotation>\u0000 </semantics></math>-variety, whose induced action is a bordism, called the pruning of the variety.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1127-1147"},"PeriodicalIF":0.8,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300586","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Strichartz estimates for the Schrödinger and wave equations with a Laguerre potential on the plane","authors":"Haoran Wang","doi":"10.1002/mana.202400168","DOIUrl":"https://doi.org/10.1002/mana.202400168","url":null,"abstract":"<p>In this paper, we obtain a set of Strichartz inequalities for solutions to the Schrödinger and wave equations with a Laguerre potential on the plane. To obtain the desired inequalities, we intend to prove the dispersive estimates for the involved Schrödinger and wave propagators and then a standard <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 <msup>\u0000 <mi>T</mi>\u0000 <mo>*</mo>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$TT^ast$</annotation>\u0000 </semantics></math> argument will enable us to arrive at these inequalities. The proof of the dispersive estimate for the Schödinger propagator relies on a crucial uniform boundedness of a series involving the Bessel functions of the first kind, while the dispersive estimate for the wave equation follows from a sequence of standard steps, such as the Gaussian boundedness of the heat kernel, Bernstein-type inequalities, and Müller–Seeger's subordination formula. We have to verify these classical results in the present setting, which is possible since the spectral properties of the involved Schrödinger operator can be explicitly calculated.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1304-1327"},"PeriodicalIF":0.8,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809867","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}

{"title":"Global existence of mild solutions for 3D stochastic Boussinesq system in Besov spaces","authors":"Jinyi Sun,&nbsp;Ning Li,&nbsp;Minghua Yang","doi":"10.1002/mana.202300526","DOIUrl":"https://doi.org/10.1002/mana.202300526","url":null,"abstract":"<p>The paper is concerned with the three-dimensional stochastic Boussinesq system driven by an additive white noise, describing the motion of viscous incompressible fluids with density stratification phenomenon in the rotational framework. By striking new balances between the smoothing effects of the Laplacian dissipation and dispersion effects caused by the Coriolis force and density stratification, we prove existence and uniqueness of global mild solutions to the three-dimensional stochastic Boussinesq system for arbitrarily large initial data and stochastic external forces in Besov spaces, provided that the stratification parameter is large enough. Our results can be regarded as a generalization of [Math. Nachr. 290(2017), 613–631] and [Indiana Univ. Math. J. 66(2017), 2037–2070].</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1105-1126"},"PeriodicalIF":0.8,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809866","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}

{"title":"On a conjecture on aCM and Ulrich sheaves on degeneracy loci","authors":"Vladimiro Benedetti,&nbsp;Fabio Tanturri","doi":"10.1002/mana.202400324","DOIUrl":"https://doi.org/10.1002/mana.202400324","url":null,"abstract":"<p>In this paper, we address a conjecture by Kleppe and Miró-Roig stating that suitable twists by line bundles (on the smooth locus) of the exterior powers of the normal sheaf of a standard determinantal locus are arithmetically Cohen–Macaulay, and even Ulrich when the locus is linear determinantal. We do so by providing a very simple locally free resolution of such sheaves obtained through the so-called Weyman's Geometric Method.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1148-1166"},"PeriodicalIF":0.8,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400324","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Comparison techniques for detection of nonoscillation in half-linear differential equations of the second order","authors":"Jaroslav Jaroš","doi":"10.1002/mana.202400107","DOIUrl":"https://doi.org/10.1002/mana.202400107","url":null,"abstract":"<p>We present a new comparison method which improves the classical Hille–Wintner theorem and its generalization to a pair of half-linear differential equations of the second order by incorporating a solution of the Riccati-type equation associated with the majorant nonoscillatory differential equation into the comparison inequality. Our results are formulated in terms of the weighted primitives of the coefficient functions of compared half-linear differential equations.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 6","pages":"2060-2071"},"PeriodicalIF":0.8,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144281556","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}

{"title":"Sharp convergence rate on Schrödingertype operators","authors":"Meng Wang,&nbsp;Shuijiang Zhao","doi":"10.1002/mana.202400266","DOIUrl":"https://doi.org/10.1002/mana.202400266","url":null,"abstract":"<p>For Schrödinger-type operators in one dimension, we consider the relationship between the convergence rate and the regularity for initial data. By establishing the associated frequency-localized maximal estimates, we prove sharp results up to the endpoints. The optimal range for the wave operator in all dimensions is also obtained.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"1082-1096"},"PeriodicalIF":0.8,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595513","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}

{"title":"Infinitesimally equivariant bundles on complex manifolds","authors":"Emile Bouaziz","doi":"10.1002/mana.202400284","DOIUrl":"https://doi.org/10.1002/mana.202400284","url":null,"abstract":"<p>We study holomorphic vector bundles equipped with a compatible action of vector field by <i>Lie derivatives</i>. We will show that the dependence of the Lie derivative on a vector field is <i>almost</i> <span></span><math>\u0000 <semantics>\u0000 <mi>O</mi>\u0000 <annotation>$mathcal {O}$</annotation>\u0000 </semantics></math>-linear. More precisely, after an algebraic reformulation, we show that any continuous <span></span><math>\u0000 <semantics>\u0000 <mi>C</mi>\u0000 <annotation>$mathbf {C}$</annotation>\u0000 </semantics></math>-linear Lie algebra splitting of the symbol map from the Atiyah algebra of a vector bundle on a complex manifold is given by a differential operator, which is further of order at most the rank of the bundle plus one. The proof is quite elementary. When the differential operator we obtain has order 0 we have simply a vector bundle with flat connection, so in a sense, our theorem says that we are always a uniformly bounded order away from this simplest case.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"1076-1081"},"PeriodicalIF":0.8,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595512","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}

{"title":"A nonlinear characterization of stochastic completeness of graphs","authors":"Marcel Schmidt,&nbsp;Ian Zimmermann","doi":"10.1002/mana.202400436","DOIUrl":"https://doi.org/10.1002/mana.202400436","url":null,"abstract":"<p>We study nonlinear Schrödinger operators on graphs. We construct minimal nonnegative solutions to corresponding semilinear elliptic equations and use them to introduce the notion of stochastic completeness at infinity in a nonlinear setting. We provide characterizations for this property in terms of a semilinear Liouville theorem. It is employed to establish a nonlinear characterization for stochastic completeness, which is a graph version of a recent result on Riemannian manifolds.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"925-943"},"PeriodicalIF":0.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400436","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Lyapunov exponents of triangular discrete time-varying systems","authors":"Adam Czornik,&nbsp;Thai Son Doan","doi":"10.1002/mana.202300373","DOIUrl":"https://doi.org/10.1002/mana.202300373","url":null,"abstract":"<p>In this paper, we present upper and lower estimates for the Lyapunov exponents of discrete linear systems with triangular time-varying coefficients. These estimates are expressed by the diagonal elements of the coefficient matrix. As a conclusion from these estimates, we also obtain bounds for the Grobman regularity coefficient.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"976-997"},"PeriodicalIF":0.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595337","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}

{"title":"Rational cohomology of \u0000 \u0000 \u0000 M\u0000 \u0000 4\u0000 ,\u0000 1\u0000 \u0000 \u0000 $mathcal {M}_{4,1}$","authors":"Yiu Man Wong,&nbsp;Angelina Zheng","doi":"10.1002/mana.202400294","DOIUrl":"https://doi.org/10.1002/mana.202400294","url":null,"abstract":"<p>We compute the rational cohomology of the moduli space <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$mathcal {M}_{4,1}$</annotation>\u0000 </semantics></math> of nonsingular genus 4 curves with one marked point, using Gorinov–Vassiliev's method.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"1041-1061"},"PeriodicalIF":0.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400294","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}