Journal de Mathematiques Pures et Appliquees最新文献_第9页

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 : 2024-11-04 DOI: 10.1016/j.matpur.2024.103620

Joaquin Moraga , Roberto Svaldi

{"title":"A geometric characterization of toric singularities","authors":"Joaquin Moraga , 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":"2024-11-04","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

A mean curvature flow arising in adversarial training 对抗训练中出现的平均曲率流

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2024-11-04 DOI: 10.1016/j.matpur.2024.103625

Leon Bungert , Tim Laux , Kerrek Stinson

引用次数: 0

A spectral dominance approach to large random matrices: Part II 大型随机矩阵的谱支配方法：第二部分

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2024-11-04 DOI: 10.1016/j.matpur.2024.103630

Charles Bertucci , Jean-Michel Lasry , Pierre-Louis Lions

引用次数: 0

A reverse Faber-Krahn inequality for the magnetic Laplacian 磁性拉普拉斯不等式的反向法布尔-克拉恩不等式

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2024-11-04 DOI: 10.1016/j.matpur.2024.103632

Bruno Colbois , Corentin Léna , Luigi Provenzano , Alessandro Savo

引用次数: 0

Monotonicity, asymptotics and level sets for principal eigenvalues of some elliptic operators with shear flow 具有剪切流的某些椭圆算子的主特征值的单调性、渐近性和水平集

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2024-11-01 DOI: 10.1016/j.matpur.2024.103622

Shuang Liu , Yuan Lou

引用次数: 0

Optimal regularity for the 2D Euler equations in the Yudovich class 尤多维奇类二维欧拉方程的最优正则性

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2024-11-01 DOI: 10.1016/j.matpur.2024.103631

Nicola De Nitti , David Meyer , Christian Seis

引用次数: 0

New perspectives on categorical Torelli theorems for del Pezzo threefolds 德尔佩佐三折的分类托雷利定理新视角

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2024-11-01 DOI: 10.1016/j.matpur.2024.103627

Soheyla Feyzbakhsh , Zhiyu Liu , Shizhuo Zhang

{"title":"New perspectives on categorical Torelli theorems for del Pezzo threefolds","authors":"Soheyla Feyzbakhsh , Zhiyu Liu , Shizhuo Zhang","doi":"10.1016/j.matpur.2024.103627","DOIUrl":"10.1016/j.matpur.2024.103627","url":null,"abstract":"<div><div>Let <span><math><msub><mrow><mi>Y</mi></mrow><mrow><mi>d</mi></mrow></msub></math></span> be a del Pezzo threefold of Picard rank one and degree <span><math><mi>d</mi><mo>≥</mo><mn>2</mn></math></span>. In this paper, we apply two different viewpoints to study <span><math><msub><mrow><mi>Y</mi></mrow><mrow><mi>d</mi></mrow></msub></math></span> via a particular admissible subcategory of its bounded derived category, called the Kuznetsov component:<ul><li><span>(i)</span><span><div>Brill–Noether reconstruction. We show that <span><math><msub><mrow><mi>Y</mi></mrow><mrow><mi>d</mi></mrow></msub></math></span> can be uniquely recovered as a Brill–Noether locus of Bridgeland stable objects in its Kuznetsov component.</div></span></li><li><span>(ii)</span><span><div>Exact equivalences. We prove that up to composing with an explicit auto-equivalence, any Fourier–Mukai type equivalence of Kuznetsov components of two del Pezzo threefolds of degree <span><math><mn>2</mn><mo>≤</mo><mi>d</mi><mo>≤</mo><mn>4</mn></math></span> can be lifted to an equivalence of their bounded derived categories. As a result, we obtain a complete description of the group of Fourier–Mukai type auto-equivalences of the Kuznetsov component of <span><math><msub><mrow><mi>Y</mi></mrow><mrow><mi>d</mi></mrow></msub></math></span>.</div></span></li></ul></div><div>In an appendix, we classify instanton sheaves on quartic double solids, generalizing a result of Druel.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"191 ","pages":"Article 103627"},"PeriodicalIF":2.1,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655418","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

Transition of the semiclassical resonance widths across a tangential crossing energy-level 切向交叉能级上半经典共振宽度的转变

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2024-11-01 DOI: 10.1016/j.matpur.2024.103634

Marouane Assal , Setsuro Fujiié , Kenta Higuchi

{"title":"Transition of the semiclassical resonance widths across a tangential crossing energy-level","authors":"Marouane Assal , Setsuro Fujiié , Kenta Higuchi","doi":"10.1016/j.matpur.2024.103634","DOIUrl":"10.1016/j.matpur.2024.103634","url":null,"abstract":"<div><div>We consider a 1D <span><math><mn>2</mn><mo>×</mo><mn>2</mn></math></span> matrix-valued operator <span><span>(1.1)</span></span> with two semiclassical Schrödinger operators on the diagonal entries and small interactions on the off-diagonal ones. When the two potentials cross at a turning point with contact order <em>n</em>, the corresponding two classical trajectories at the crossing level intersect at one point in the phase space with contact order 2<em>n</em>. Below this level, they have no intersection, which suggests exponentially small widths of resonances (see e.g., <span><span>[1]</span></span>, <span><span>[2]</span></span>), while above this level, on the contrary, they intersect at two points, which implies a polynomial order of the widths as proved in <span><span>[3]</span></span>. We prove that the transition of the resonance widths near the crossing level is described in terms of a generalized Airy function. This result generalizes <span><span>[4]</span></span> to the tangential crossing and <span><span>[3]</span></span> to the crossing at a turning point. Our approach is based on the computation of the microlocal transfer matrix at the crossing point between the incoming and outgoing microlocal solutions.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"191 ","pages":"Article 103634"},"PeriodicalIF":2.1,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655424","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

Existence and stability of almost finite energy weak solutions to the quantum Euler-Maxwell system 量子欧拉-麦克斯韦系统的几乎有限能量弱解的存在性和稳定性

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2024-11-01 DOI: 10.1016/j.matpur.2024.103629

Paolo Antonelli , Pierangelo Marcati , Raffaele Scandone

{"title":"Existence and stability of almost finite energy weak solutions to the quantum Euler-Maxwell system","authors":"Paolo Antonelli , Pierangelo Marcati , Raffaele Scandone","doi":"10.1016/j.matpur.2024.103629","DOIUrl":"10.1016/j.matpur.2024.103629","url":null,"abstract":"<div><div>In this paper we prove the existence of global in time, finite energy weak solutions to the quantum magnetohydrodynamics (QMHD) system, for a large class of initial data that are slightly more regular than being of finite energy. No restriction is given on their size or the uniform positivity of the mass density. The QMHD system is a well-established model in superconductivity due to Feynman, and is intimately related to a nonlinear Maxwell-Schrödinger (NLMS) system via the Madelung transformations. The lack of global well-posedness (GWP) results for the NLMS system in the energy norm provides an obstruction to stability of its solutions, and consequently to the use of approximation arguments to make rigorous the Madelung approach. We implement here a new strategy, that derives weak solutions to QMHD starting from weak solutions to NLMS, by exploiting its Duhamel formulation. This derivation is rigorously justified by means of suitable dispersive/smoothing estimates for almost finite energy weak solutions to NLMS. The corresponding weak solutions to QMHD satisfy a generalized irrotationality condition, that allows for the presence of non-trivial vorticity (e.g., vortex filaments) concentrated in the vacuum region. This is in sharp contrast with the Euler-Maxwell system where the dispersion is not able to deal with the vorticity transport, therefore almost GWP (for regular solutions that are small perturbations of constant states) holds only in a lifespan, reciprocal of the size of the initial vorticity. Moreover, we also prove a stability property in the energy norm of the weak solutions constructed by our approach. This result follows from new local smoothing estimates for NLMS that are also of independent interest. As a byproduct, we also show the stability for the electromagnetic Lorentz force.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"191 ","pages":"Article 103629"},"PeriodicalIF":2.1,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655421","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

The soliton resolution conjecture for the Boussinesq equation 布辛斯克方程的孤子解析猜想

IF 2.1 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2024-11-01 DOI: 10.1016/j.matpur.2024.103621

C. Charlier , J. Lenells

引用次数: 0