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Fano 4-folds with $b_{2}>12$ are products of surfaces b_{2}>12$的法诺4折叠是曲面的乘积
IF 3.1 1区 数学
Inventiones mathematicae Pub Date : 2024-02-05 DOI: 10.1007/s00222-024-01236-6
C. Casagrande
{"title":"Fano 4-folds with $b_{2}>12$ are products of surfaces","authors":"C. Casagrande","doi":"10.1007/s00222-024-01236-6","DOIUrl":"https://doi.org/10.1007/s00222-024-01236-6","url":null,"abstract":"<p>Let <span>(X)</span> be a smooth, complex Fano 4-fold, and <span>(rho _{X})</span> its Picard number. We show that if <span>(rho _{X}&gt;12)</span>, then <span>(X)</span> is a product of del Pezzo surfaces. The proof relies on a careful study of divisorial elementary contractions <span>(fcolon Xto Y)</span> such that <span>(dim f(operatorname{Exc}(f))=2)</span>, together with the author’s previous work on Fano 4-folds. In particular, given <span>(fcolon Xto Y)</span> as above, under suitable assumptions we show that <span>(S:=f(operatorname{Exc}(f)))</span> is a smooth del Pezzo surface with <span>(-K_{S}=(-K_{Y})_{|S})</span>.</p>","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139751571","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
SRB measures for $C^{infty }$ surface diffeomorphisms C^{infty }$ 表面差分的 SRB 量纲
IF 3.1 1区 数学
Inventiones mathematicae Pub Date : 2024-02-05 DOI: 10.1007/s00222-024-01235-7
{"title":"SRB measures for $C^{infty }$ surface diffeomorphisms","authors":"","doi":"10.1007/s00222-024-01235-7","DOIUrl":"https://doi.org/10.1007/s00222-024-01235-7","url":null,"abstract":"<h3>Abstract</h3> <p>A <span> <span>(C^{infty })</span> </span> smooth surface diffeomorphism admits an SRB measure if and only if the set <span> <span>({ x, limsup _{n}frac{1}{n}log |d_{x}f^{n}|&gt;0})</span> </span> has positive Lebesgue measure. Moreover the basins of the ergodic SRB measures are covering this set Lebesgue almost everywhere. We also obtain similar results for <span> <span>(C^{r})</span> </span> surface diffeomorphisms with <span> <span>(+infty &gt;r&gt;1)</span> </span>.</p>","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139751573","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 phantom on a rational surface 理性表面上的幻影
IF 3.1 1区 数学
Inventiones mathematicae Pub Date : 2023-12-21 DOI: 10.1007/s00222-023-01234-0
Johannes Krah
{"title":"A phantom on a rational surface","authors":"Johannes Krah","doi":"10.1007/s00222-023-01234-0","DOIUrl":"https://doi.org/10.1007/s00222-023-01234-0","url":null,"abstract":"<p>We construct a non-full exceptional collection of maximal length consisting of line bundles on the blow-up of the projective plane in 10 general points. As a consequence, the orthogonal complement of this collection is a universal phantom category. This provides a counterexample to a conjecture of Kuznetsov and to a conjecture of Orlov.</p>","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139029892","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
An approximate form of Artin’s holomorphy conjecture and non-vanishing of Artin $L$ -functions 阿尔丁全态猜想的近似形式和阿尔丁 $L$ 函数的非凡性
IF 3.1 1区 数学
Inventiones mathematicae Pub Date : 2023-12-12 DOI: 10.1007/s00222-023-01232-2
Robert J. Lemke Oliver, Jesse Thorner, Asif Zaman
{"title":"An approximate form of Artin’s holomorphy conjecture and non-vanishing of Artin $L$ -functions","authors":"Robert J. Lemke Oliver, Jesse Thorner, Asif Zaman","doi":"10.1007/s00222-023-01232-2","DOIUrl":"https://doi.org/10.1007/s00222-023-01232-2","url":null,"abstract":"<p>Let <span>(k)</span> be a number field and <span>(G)</span> be a finite group. Let <span>(mathfrak{F}_{k}^{G}(Q))</span> be the family of number fields <span>(K)</span> with absolute discriminant <span>(D_{K})</span> at most <span>(Q)</span> such that <span>(K/k)</span> is normal with Galois group isomorphic to <span>(G)</span>. If <span>(G)</span> is the symmetric group <span>(S_{n})</span> or any transitive group of prime degree, then we unconditionally prove that for all <span>(Kin mathfrak{F}_{k}^{G}(Q))</span> with at most <span>(O_{varepsilon }(Q^{varepsilon }))</span> exceptions, the <span>(L)</span>-functions associated to the faithful Artin representations of <span>(mathrm{Gal}(K/k))</span> have a region of holomorphy and non-vanishing commensurate with predictions by the Artin conjecture and the generalized Riemann hypothesis. This result is a special case of a more general theorem. As applications, we prove that: </p><ol>\u0000<li>\u0000<span>(1)</span>\u0000<p>there exist infinitely many degree <span>(n)</span> <span>(S_{n})</span>-fields over ℚ whose class group is as large as the Artin conjecture and GRH imply, settling a question of Duke;</p>\u0000</li>\u0000<li>\u0000<span>(2)</span>\u0000<p>for a prime <span>(p)</span>, the periodic torus orbits attached to the ideal classes of almost all totally real degree <span>(p)</span> fields <span>(F)</span> over ℚ equidistribute on <span>(mathrm{PGL}_{p}(mathbb{Z})backslash mathrm{PGL}_{p}(mathbb{R}))</span> with respect to Haar measure;</p>\u0000</li>\u0000<li>\u0000<span>(3)</span>\u0000<p>for each <span>(ell geq 2)</span>, the <span>(ell )</span>-torsion subgroups of the ideal class groups of almost all degree <span>(p)</span> fields over <span>(k)</span> (resp. almost all degree <span>(n)</span> <span>(S_{n})</span>-fields over <span>(k)</span>) are as small as GRH implies; and</p>\u0000</li>\u0000<li>\u0000<span>(4)</span>\u0000<p>an effective variant of the Chebotarev density theorem holds for almost all fields in such families.</p>\u0000</li>\u0000</ol>","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885485","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
CAT(0) spaces of higher rank II 高阶 II CAT(0) 空间
IF 3.1 1区 数学
Inventiones mathematicae Pub Date : 2023-12-08 DOI: 10.1007/s00222-023-01230-4
Stephan Stadler
{"title":"CAT(0) spaces of higher rank II","authors":"Stephan Stadler","doi":"10.1007/s00222-023-01230-4","DOIUrl":"https://doi.org/10.1007/s00222-023-01230-4","url":null,"abstract":"<p>This belongs to a series of papers motivated by Ballmann’s Higher Rank Rigidity Conjecture. We prove the following. Let <span>(X)</span> be a CAT(0) space with a geometric group action <span>(Gamma curvearrowright X)</span>. Suppose that every geodesic in <span>(X)</span> lies in an <span>(n)</span>-flat, <span>(ngeq 2)</span>. If <span>(X)</span> contains a periodic <span>(n)</span>-flat which does not bound a flat <span>((n+1))</span>-half-space, then <span>(X)</span> is a Riemannian symmetric space, a Euclidean building or non-trivially splits as a metric product. This generalizes the Higher Rank Rigidity Theorem for Hadamard manifolds with geometric group actions.</p>","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138553364","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
Effective equidistribution for multiplicative Diophantine approximation on lines 线段上乘法二叉近似的有效等差数列
IF 3.1 1区 数学
Inventiones mathematicae Pub Date : 2023-12-08 DOI: 10.1007/s00222-023-01233-1
Sam Chow, Lei Yang
{"title":"Effective equidistribution for multiplicative Diophantine approximation on lines","authors":"Sam Chow, Lei Yang","doi":"10.1007/s00222-023-01233-1","DOIUrl":"https://doi.org/10.1007/s00222-023-01233-1","url":null,"abstract":"<p>Given any line in the plane, we strengthen the Littlewood conjecture by two logarithms for almost every point on the line, thereby generalising the fibre result of Beresnevich, Haynes, and Velani. To achieve this, we prove an effective asymptotic equidistribution result for one-parameter unipotent orbits in <span>({mathrm{SL}}(3, {mathbb{R}})/{mathrm{SL}}(3,{mathbb{Z}}))</span>. We also provide a complementary convergence statement, by developing the structural theory of dual Bohr sets: at the cost of a slightly stronger Diophantine assumption, this sharpens a result of Kleinbock’s from 2003. Finally, we refine the theory of logarithm laws in homogeneous spaces.</p>","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885484","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
The time-like minimal surface equation in Minkowski space: low regularity solutions 闵科夫斯基空间中的类时间极小曲面方程：低正则解
IF 3.1 1区 数学
Inventiones mathematicae Pub Date : 2023-12-07 DOI: 10.1007/s00222-023-01231-3
Albert Ai, Mihaela Ifrim, Daniel Tataru
{"title":"The time-like minimal surface equation in Minkowski space: low regularity solutions","authors":"Albert Ai, Mihaela Ifrim, Daniel Tataru","doi":"10.1007/s00222-023-01231-3","DOIUrl":"https://doi.org/10.1007/s00222-023-01231-3","url":null,"abstract":"<p>It has long been conjectured that for nonlinear wave equations that satisfy a nonlinear form of the null condition, the low regularity well-posedness theory can be significantly improved compared to the sharp results of Smith-Tataru for the generic case. The aim of this article is to prove the first result in this direction, namely for the time-like minimal surface equation in the Minkowski space-time. Further, our improvement is substantial, namely by <span>(3/8)</span> derivatives in two space dimensions and by <span>(1/4)</span> derivatives in higher dimensions.</p>","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138559679","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: 4
Scalar curvature rigidity of convex polytopes 凸多边形的标量曲率刚性
IF 3.1 1区 数学
Inventiones mathematicae Pub Date : 2023-11-29 DOI: 10.1007/s00222-023-01229-x
Simon Brendle
{"title":"Scalar curvature rigidity of convex polytopes","authors":"Simon Brendle","doi":"10.1007/s00222-023-01229-x","DOIUrl":"https://doi.org/10.1007/s00222-023-01229-x","url":null,"abstract":"<p>We prove a scalar curvature rigidity theorem for convex polytopes. The proof uses the Fredholm theory for Dirac operators on manifolds with boundary. A variant of a theorem of Fefferman and Phong plays a central role in our analysis.</p>","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508493","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: 3
Derivation of Kubo’s formula for disordered systems at zero temperature 零温度下无序系统的Kubo公式的推导
IF 3.1 1区 数学
Inventiones mathematicae Pub Date : 2023-11-28 DOI: 10.1007/s00222-023-01227-z
Wojciech De Roeck, Alexander Elgart, Martin Fraas
{"title":"Derivation of Kubo’s formula for disordered systems at zero temperature","authors":"Wojciech De Roeck, Alexander Elgart, Martin Fraas","doi":"10.1007/s00222-023-01227-z","DOIUrl":"https://doi.org/10.1007/s00222-023-01227-z","url":null,"abstract":"<p>This work justifies the linear response formula for the Hall conductance of a two-dimensional disordered system. The proof rests on controlling the dynamics associated with a random time-dependent Hamiltonian.</p><p>The principal challenge is related to the fact that spectral and dynamical localization are intrinsically unstable under perturbation, and the exact spectral flow - the tool used previously to control the dynamics in this context - does not exist. We resolve this problem by proving a local adiabatic theorem: With high probability, the physical evolution of a localized eigenstate <span>(psi )</span> associated with a random system remains close to the spectral flow for a restriction of the instantaneous Hamiltonian to a region <span>(R)</span> where the bulk of <span>(psi )</span> is supported. Allowing <span>(R)</span> to grow at most logarithmically in time ensures that the deviation of the physical evolution from this spectral flow is small.</p><p>To substantiate our claim on the failure of the global spectral flow in disordered systems, we prove eigenvector hybridization in a one-dimensional Anderson model at all scales.</p>","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508484","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
Higher Siegel–Weil formula for unitary groups: the non-singular terms 酉群的高Siegel-Weil公式:非奇异项
IF 3.1 1区 数学
Inventiones mathematicae Pub Date : 2023-11-27 DOI: 10.1007/s00222-023-01228-y
Tony Feng, Zhiwei Yun, Wei Zhang
{"title":"Higher Siegel–Weil formula for unitary groups: the non-singular terms","authors":"Tony Feng, Zhiwei Yun, Wei Zhang","doi":"10.1007/s00222-023-01228-y","DOIUrl":"https://doi.org/10.1007/s00222-023-01228-y","url":null,"abstract":"<p>We construct special cycles on the moduli stack of hermitian shtukas. We prove an identity between (1) the <span>(r^{mathrm{th}})</span> central derivative of non-singular Fourier coefficients of a normalized Siegel–Eisenstein series, and (2) the degree of special cycles of “virtual dimension 0” on the moduli stack of hermitian shtukas with <span>(r)</span> legs. This may be viewed as a function-field analogue of the Kudla-Rapoport Conjecture, that has the additional feature of encompassing all higher derivatives of the Eisenstein series.</p>","PeriodicalId":14429,"journal":{"name":"Inventiones mathematicae","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508483","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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