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Derived categories of symmetric products and moduli spaces of vector bundles on a curve 曲线上向量束的对称积和模空间的导出范畴
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-05-01 Epub Date: 2025-02-24 DOI: 10.1016/j.matpur.2025.103694
Kyoung-Seog Lee , Han-Bom Moon
{"title":"Derived categories of symmetric products and moduli spaces of vector bundles on a curve","authors":"Kyoung-Seog Lee ,&nbsp;Han-Bom Moon","doi":"10.1016/j.matpur.2025.103694","DOIUrl":"10.1016/j.matpur.2025.103694","url":null,"abstract":"<div><div>We show that the derived categories of symmetric products of a curve are embedded into the derived categories of the moduli spaces of vector bundles of large ranks on the curve. It supports a prediction of the existence of a semiorthogonal decomposition of the derived category of the moduli space, expected by a motivic computation. As an application, we show that all Jacobian varieties, symmetric products of curves, and all principally polarized abelian varieties of dimension at most three, are Fano visitors. We also obtain similar results for motives.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"197 ","pages":"Article 103694"},"PeriodicalIF":2.1,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Four-dimensional gradient Ricci solitons with (half) nonnegative isotropic curvature 具有（半）非负各向同性曲率的四维梯度里奇孤子
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-05-01 Epub Date: 2025-02-24 DOI: 10.1016/j.matpur.2025.103686
Huai-Dong Cao , Junming Xie
{"title":"Four-dimensional gradient Ricci solitons with (half) nonnegative isotropic curvature","authors":"Huai-Dong Cao ,&nbsp;Junming Xie","doi":"10.1016/j.matpur.2025.103686","DOIUrl":"10.1016/j.matpur.2025.103686","url":null,"abstract":"<div><div>This is a sequel to our paper <span><span>[24]</span></span>, in which we investigated the geometry of 4-dimensional gradient shrinking Ricci solitons with half positive (nonnegative) isotropic curvature. In this paper, we mainly focus on 4-dimensional gradient steady Ricci solitons with nonnegative isotropic curvature (WPIC) or half nonnegative isotropic curvature (half WPIC). In particular, for 4D complete <em>ancient solutions</em> with WPIC, we are able to prove the 2-nonnegativity of the Ricci curvature and bound the curvature tensor <em>Rm</em> by <span><math><mo>|</mo><mi>R</mi><mi>m</mi><mo>|</mo><mo>≤</mo><mi>R</mi></math></span>. For 4D gradient steady solitons with WPIC, we obtain a classification result. We also give a partial classification of 4D gradient steady Ricci solitons with half WPIC. Moreover, we obtain a preliminary classification result for 4D complete gradient <em>expanding Ricci solitons</em> with WPIC. Finally, motivated by the recent work <span><span>[59]</span></span>, we improve our earlier results in <span><span>[24]</span></span> on 4D gradient <em>shrinking Ricci solitons</em> with half PIC or half WPIC, and also provide a characterization of complete gradient Kähler-Ricci shrinkers in complex dimension two among 4-dimensional gradient Ricci shrinkers.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"197 ","pages":"Article 103686"},"PeriodicalIF":2.1,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Reconstruction along a geodesic from sphere data in Finsler geometry and anisotropic elasticity 基于Finsler几何和各向异性弹性的球面数据沿测地线重建
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-04-01 Epub Date: 2025-02-24 DOI: 10.1016/j.matpur.2025.103688
Maarten V. de Hoop , Joonas Ilmavirta , Matti Lassas
{"title":"Reconstruction along a geodesic from sphere data in Finsler geometry and anisotropic elasticity","authors":"Maarten V. de Hoop ,&nbsp;Joonas Ilmavirta ,&nbsp;Matti Lassas","doi":"10.1016/j.matpur.2025.103688","DOIUrl":"10.1016/j.matpur.2025.103688","url":null,"abstract":"<div><div>Dix formulated the inverse problem of recovering an elastic body from the measurements of wave fronts of point sources. We geometrize this problem in the context of seismology, leading to the geometrical inverse problem of recovering a Finsler manifold from certain sphere data in a given open subset of the manifold. We solve this problem locally along any geodesic through the measurement set.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"196 ","pages":"Article 103688"},"PeriodicalIF":2.1,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143507519","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Commutator type and Levi type of a system of CR vector fields CR矢量场系统的换向子型和李维型
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-04-01 Epub Date: 2025-02-24 DOI: 10.1016/j.matpur.2025.103693
Xiaojun Huang , Wanke Yin
{"title":"Commutator type and Levi type of a system of CR vector fields","authors":"Xiaojun Huang ,&nbsp;Wanke Yin","doi":"10.1016/j.matpur.2025.103693","DOIUrl":"10.1016/j.matpur.2025.103693","url":null,"abstract":"<div><div>Let <em>M</em> be a smooth pseudoconvex real hypersurface in <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> with <span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span> and let <em>B</em> be a subbundle of the CR tangent vector bundle of <em>M</em>. We prove that the commutator type and the Levi type associated with <em>B</em> are the same when either of them is less than 8. When the Levi type is eight or larger, we show that it is bounded from above by twice of the commutator type minus 8. Our results provide a partial solution to a generalized conjecture of D'Angelo.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"196 ","pages":"Article 103693"},"PeriodicalIF":2.1,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143507536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Frequency-domain criterion on the stabilizability for infinite-dimensional linear control systems 无穷维线性控制系统稳定性的频域判据
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-04-01 Epub Date: 2025-02-24 DOI: 10.1016/j.matpur.2025.103690
Karl Kunisch , Gengsheng Wang , Huaiqiang Yu
{"title":"Frequency-domain criterion on the stabilizability for infinite-dimensional linear control systems","authors":"Karl Kunisch ,&nbsp;Gengsheng Wang ,&nbsp;Huaiqiang Yu","doi":"10.1016/j.matpur.2025.103690","DOIUrl":"10.1016/j.matpur.2025.103690","url":null,"abstract":"<div><div>A quantitative frequency-domain condition related to the exponential stabilizability for infinite-dimensional linear control systems is presented. It is proven that this condition is necessary and sufficient for the stabilizability of special systems, while it is a necessary condition for the stabilizability in general. Applications are provided.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"196 ","pages":"Article 103690"},"PeriodicalIF":2.1,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143507535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Damping for fractional wave equations and applications to water waves 分数波方程的阻尼及其在水波中的应用
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-04-01 Epub Date: 2025-02-24 DOI: 10.1016/j.matpur.2025.103692
Thomas Alazard , Jeremy L. Marzuola , Jian Wang
{"title":"Damping for fractional wave equations and applications to water waves","authors":"Thomas Alazard ,&nbsp;Jeremy L. Marzuola ,&nbsp;Jian Wang","doi":"10.1016/j.matpur.2025.103692","DOIUrl":"10.1016/j.matpur.2025.103692","url":null,"abstract":"<div><div>Motivated by numerically modeling surface waves for inviscid Euler equations, we analyze linear models for damped water waves and establish decay properties for the energy for sufficiently regular initial configurations. Our findings give the explicit decay rates for the energy, but do not address reflection/transmission of waves at the interface of the damping. Still for a subset of the models considered, this represents the first result proving the decay of the energy of the surface wave models.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"196 ","pages":"Article 103692"},"PeriodicalIF":2.1,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143529175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A geometric characterization of toric singularities 环面奇点的几何表征
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-03-01 Epub Date: 2024-11-04 DOI: 10.1016/j.matpur.2024.103620
Joaquin Moraga , Roberto Svaldi
{"title":"A geometric characterization of toric singularities","authors":"Joaquin Moraga ,&nbsp;Roberto Svaldi","doi":"10.1016/j.matpur.2024.103620","DOIUrl":"10.1016/j.matpur.2024.103620","url":null,"abstract":"<div><div>Given a projective contraction <span><math><mi>π</mi><mo>:</mo><mi>X</mi><mo>→</mo><mi>Z</mi></math></span> and a log canonical pair <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></span> such that <span><math><mo>−</mo><mo>(</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>+</mo><mi>B</mi><mo>)</mo></math></span> is nef over a neighborhood of a closed point <span><math><mi>z</mi><mo>∈</mo><mi>Z</mi></math></span>, one can define an invariant, the complexity of <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></span> over <span><math><mi>z</mi><mo>∈</mo><mi>Z</mi></math></span>, comparing the dimension of <em>X</em> and the relative Picard number of <span><math><mi>X</mi><mo>/</mo><mi>Z</mi></math></span> with the sum of the coefficients of those components of <em>B</em> intersecting the fiber over <em>z</em>. We prove that, in the hypotheses above, the complexity of the log pair <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></span> over <span><math><mi>z</mi><mo>∈</mo><mi>Z</mi></math></span> is non-negative and that when it is zero then <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mo>⌊</mo><mi>B</mi><mo>⌋</mo><mo>)</mo><mo>→</mo><mi>Z</mi></math></span> is formally isomorphic to a morphism of toric varieties around <span><math><mi>z</mi><mo>∈</mo><mi>Z</mi></math></span>. In particular, considering the case when <em>π</em> is the identity morphism, we get a geometric characterization of singularities that are formally isomorphic to toric singularities, thus resolving a conjecture due to Shokurov.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"195 ","pages":"Article 103620"},"PeriodicalIF":2.1,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143155111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Construction of weak solutions to a model of pressureless viscous flow driven by nonlocal attraction–repulsion 非局部吸引-排斥驱动无压粘性流动模型弱解的构造
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-03-01 Epub Date: 2025-01-15 DOI: 10.1016/j.matpur.2025.103671
Piotr B. Mucha , Maja Szlenk , Ewelina Zatorska
{"title":"Construction of weak solutions to a model of pressureless viscous flow driven by nonlocal attraction–repulsion","authors":"Piotr B. Mucha ,&nbsp;Maja Szlenk ,&nbsp;Ewelina Zatorska","doi":"10.1016/j.matpur.2025.103671","DOIUrl":"10.1016/j.matpur.2025.103671","url":null,"abstract":"<div><div>We analyze the pressureless Navier-Stokes system with nonlocal attraction–repulsion forces. Such systems appear in the context of models of collective behaviour. We prove the existence of weak solutions on the whole space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> in the case of density-dependent degenerate viscosity. For the nonlocal term it is assumed that the interaction kernel has the quadratic growth at infinity and almost quadratic singularity at zero. Under these assumptions, we derive the analog of the Bresch–Desjardins and Mellet–Vasseur estimates for the nonlocal system. In particular, we are able to adapt the approach of Vasseur and Yu <span><span>[37]</span></span>, <span><span>[36]</span></span> to construct a weak solution.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"195 ","pages":"Article 103671"},"PeriodicalIF":2.1,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143155109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Infinitesimal conformal restriction and unitarizing measures for Virasoro algebra Virasoro代数的无穷小共形限制和统一措施
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-03-01 Epub Date: 2025-01-15 DOI: 10.1016/j.matpur.2025.103669
Maria Gordina , Wei Qian , Yilin Wang
{"title":"Infinitesimal conformal restriction and unitarizing measures for Virasoro algebra","authors":"Maria Gordina ,&nbsp;Wei Qian ,&nbsp;Yilin Wang","doi":"10.1016/j.matpur.2025.103669","DOIUrl":"10.1016/j.matpur.2025.103669","url":null,"abstract":"<div><div>We use the SLE<sub><em>κ</em></sub> loop measure to construct a natural representation of the Virasoro algebra of central charge <span><math><mi>c</mi><mo>=</mo><mi>c</mi><mo>(</mo><mi>κ</mi><mo>)</mo><mo>≤</mo><mn>1</mn></math></span>. In particular, we introduce a non-degenerate bilinear Hermitian form (and non positive-definite) using the SLE loop measure and show that the representation is indefinite unitary. Our proof relies on the infinitesimal conformal restriction property of the SLE loop measure.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"195 ","pages":"Article 103669"},"PeriodicalIF":2.1,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143155110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Non-linear operator-valued elliptic flows with application to quantum field theory 非线性算子值椭圆流及其在量子场论中的应用
IF 2.1 1区 数学
Journal de Mathematiques Pures et Appliquees Pub Date : 2025-03-01 Epub Date: 2025-01-15 DOI: 10.1016/j.matpur.2025.103657
Jean-Bernard Bru , Nathan Metraud
{"title":"Non-linear operator-valued elliptic flows with application to quantum field theory","authors":"Jean-Bernard Bru ,&nbsp;Nathan Metraud","doi":"10.1016/j.matpur.2025.103657","DOIUrl":"10.1016/j.matpur.2025.103657","url":null,"abstract":"<div><div>Differential equations on spaces of operators are very little developed in Mathematics, being in general very challenging. Here, we study a novel system of such (non-linear) differential equations. We show it has a unique solution for all times, for instance in the Schatten norm topology. This system presents remarkable ellipticity properties that turn out to be crucial for the study of the infinite-time limit of its solution, which is proven under relatively weak, albeit probably not necessary, hypotheses on the initial data. This system of differential equations is the elliptic counterpart of an hyperbolic flow applied to quantum field theory to diagonalize Hamiltonians that are quadratic in the bosonic field. In a similar way, this elliptic flow, in particular its asymptotics, has application in quantum field theory: it can be used to diagonalize Hamiltonians that are quadratic in the fermionic field while giving new explicit expressions and properties of these pivotal Hamiltonians of quantum field theory and quantum statistical mechanics.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"195 ","pages":"Article 103657"},"PeriodicalIF":2.1,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143155106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","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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