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Annales Scientifiques De L Ecole Normale Superieure最新文献

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Semiclassical diffraction by conormal potential singularities 法向势奇点的半经典衍射
1区 数学
Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2023-10-02 DOI: 10.24033/asens.2543
Oran Gannot, Jared Wunsch
{"title":"Semiclassical diffraction by conormal potential singularities","authors":"Oran Gannot, Jared Wunsch","doi":"10.24033/asens.2543","DOIUrl":"https://doi.org/10.24033/asens.2543","url":null,"abstract":"We establish propagation of singularities for the semiclassical Schrodinger equation, where the potential is conormal to a hypersurface. We show that semiclassical wavefront set propagates along generalized broken bicharacteristics, hence reflection of singularities may occur along trajectories reaching the hypersurface transversely. The reflected wavefront set is weaker, however, by a power of $h$ that depends on the regularity of the potential. We also show that for sufficiently regular potentials, wavefront set may not stick to the hypersurface, but rather detaches from it at points of tangency to travel along ordinary bicharacteristics.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135790683","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: 9
On bulk deviations for the local behavior of random interlacements 随机交错局部行为的总体偏差
1区 数学
Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2023-10-02 DOI: 10.24033/asens.2544
Alain-Sol Sznitman
{"title":"On bulk deviations for the local behavior of random interlacements","authors":"Alain-Sol Sznitman","doi":"10.24033/asens.2544","DOIUrl":"https://doi.org/10.24033/asens.2544","url":null,"abstract":"We investigate certain large deviation asymptotics concerning random interlacements in Z^d, d bigger or equal to 3. We find the principal exponential rate of decay for the probability that the average value of some suitable non-decreasing local function of the field of occupation times, sampled at each point of a large box, exceeds its expected value. We express the exponential rate of decay in terms of a constrained minimum for the Dirichlet energy of functions on R^d that decay at infinity. An application concerns the excess presence of random interlacements in a large box. Our findings exhibit similarities to some of the results of van den Berg-Bolthausen-den Hollander in their work on moderate deviations of the volume of the Wiener sausage. An other application relates to recent work of the author on macroscopic holes in connected components of the vacant set in arXiv:1802.05255v2.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135790684","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: 11
Bounding the Betti numbers of real hypersurfaces near the tropical limit 靠近热带极限的实超曲面的贝蒂数边界
1区 数学
Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2023-10-02 DOI: 10.24033/asens.2547
Arthur Renaudineau, Kristin Shaw
{"title":"Bounding the Betti numbers of real hypersurfaces near the tropical limit","authors":"Arthur Renaudineau, Kristin Shaw","doi":"10.24033/asens.2547","DOIUrl":"https://doi.org/10.24033/asens.2547","url":null,"abstract":"We prove a bound conjectured by Itenberg on the Betti numbers of real algebraic hypersurfaces near non-singular tropical limits. These bounds are given in terms of the Hodge numbers of the complexification. To prove the conjecture we introduce a real variant of tropical homology and define a filtration on the corresponding chain complex inspired by Kalinin's filtration. The spectral sequence associated to this filtration converges to the homology groups of the real algebraic variety and we show that the terms of the first page are tropical homology groups with $mathbb{Z}_2$-coefficients. The dimensions of these homology groups correspond to the Hodge numbers of complex projective hypersurfaces. The bounds on the Betti numbers of the real part follow, as well as a criterion to obtain a maximal variety. We also generalise a known formula relating the signature of the complex hypersurface and the Euler characteristic of the real algebraic hypersurface, as well as Haas' combinatorial criterion for the maximality of plane curves near the tropical limit.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135790680","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: 22
On the algebraic cobordism ring of involutions 关于对合的代数协环
1区 数学
Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2023-10-02 DOI: 10.24033/asens.2548
Olivier Haution
{"title":"On the algebraic cobordism ring of involutions","authors":"Olivier Haution","doi":"10.24033/asens.2548","DOIUrl":"https://doi.org/10.24033/asens.2548","url":null,"abstract":"We consider the cobordism ring of involutions of a field of characteristic not two, whose elements are formal differences of classes of smooth projective varieties equipped with an involution, and relations arise from equivariant K-theory characteristic numbers. We investigate in detail the structure of this ring. Concrete applications are provided concerning involutions of varieties, relating the geometry of the ambient variety to that of the fixed locus, in terms of Chern numbers. In particular, we prove an algebraic analog of Boardman's five halves theorem in topology, of which we provide several generalisations and variations.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135790098","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
Cyclotomic double affine Hecke algebras 双仿射Hecke代数
IF 1.9 1区 数学
Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2020-12-08 DOI: 10.24033/ASENS.2446
Braverman Alexander, V. F. Mikhail, Etingof Pavel
{"title":"Cyclotomic double affine Hecke algebras","authors":"Braverman Alexander, V. F. Mikhail, Etingof Pavel","doi":"10.24033/ASENS.2446","DOIUrl":"https://doi.org/10.24033/ASENS.2446","url":null,"abstract":"We show that the partially spherical cyclotomic rational Cherednik algebra (obtained from the full rational Cherednik algebra by averaging out the cyclotomic part of the underlying reflection group) has four other descriptions: (1) as a subalgebra of the degenerate DAHA of type A given by generators; (2) as an algebra given by generators and relations; (3) as an algebra of differential-reflection operators preserving some spaces of functions; (4) as equivariant Borel-Moore homology of a certain variety. Also, we define a new $q$-deformation of this algebra, which we call cyclotomic DAHA. Namely, we give a $q$-deformation of each of the above four descriptions of the partially spherical rational Cherednik algebra, replacing differential operators with difference operators, degenerate DAHA with DAHA, and homology with K-theory, and show that they give the same algebra. In addition, we show that spherical cyclotomic DAHA are quantizations of certain multiplicative quiver and bow varieties, which may be interpreted as K-theoretic Coulomb branches of a framed quiver gauge theory. Finally, we apply cyclotomic DAHA to prove new flatness results for various kinds of spaces of $q$-deformed quasiinvariants. In the appendix by H. Nakajima and D. Yamakawa (added in version 2), the authors explain the relations between multiplicative bow varieties and (various versions of) multiplicative quiver varieties for a cyclic quiver.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"8 1","pages":"1249-1312"},"PeriodicalIF":1.9,"publicationDate":"2020-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86368993","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: 15
Higher dimensional formal loop spaces 高维形式循环空间
IF 1.9 1区 数学
Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2020-10-20 DOI: 10.24033/asens.2329
Benjamin Hennion
{"title":"Higher dimensional formal loop spaces","authors":"Benjamin Hennion","doi":"10.24033/asens.2329","DOIUrl":"https://doi.org/10.24033/asens.2329","url":null,"abstract":"If $M$ is a symplectic manifold then the space of smooth loops $mathrm C^{infty}(mathrm S^1,M)$ inherits of a quasi-symplectic form. We will focus in this article on an algebraic analogue of that result. In 2004, Kapranov and Vasserot introduced and studied the formal loop space of a scheme $X$. \u0000We generalize their construction to higher dimensional loops. To any scheme $X$ -- not necessarily smooth -- we associate $mathcal L^d(X)$, the space of loops of dimension $d$. We prove it has a structure of (derived) Tate scheme -- ie its tangent is a Tate module: it is infinite dimensional but behaves nicely enough regarding duality. We also define the bubble space $mathcal B^d(X)$, a variation of the loop space. We prove that $mathcal B^d(X)$ is endowed with a natural symplectic form as soon as $X$ has one (in the sense of [PTVV]). \u0000Throughout this paper, we will use the tools of $(infty,1)$-categories and symplectic derived algebraic geometry.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"39 1","pages":"609-663"},"PeriodicalIF":1.9,"publicationDate":"2020-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79853028","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: 10
Tropical cycle classes for non-archimedean spaces and weight decomposition of De Rham cohomology sheaves 非阿基米德空间的热带旋回类和De Rham上同轴的权分解
IF 1.9 1区 数学
Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2020-01-01 DOI: 10.24033/asens.2423
Yifeng Liu
{"title":"Tropical cycle classes for non-archimedean spaces and weight decomposition of De Rham cohomology sheaves","authors":"Yifeng Liu","doi":"10.24033/asens.2423","DOIUrl":"https://doi.org/10.24033/asens.2423","url":null,"abstract":"This article has three major goals. First, we define tropical cycle class maps for smooth varieties over non-Archimedean fields, valued in the Dolbeault cohomology defined in terms of real forms introduced by Chambert-Loir and Ducros. Second, we construct a functorial decomposition of de Rham cohomology sheaves, called weight decomposition, for smooth analytic spaces over certain non-Archimedean fields of characteristic zero, which generalizes a construction of Berkovich and solves a question raised by himself. Third, we reveal a connection between the tropical theory and the algebraic de Rham theory. As an application, we show that algebraic cycles that are trivial in the algebraic de Rham cohomology are trivial as currents for Dolbeault cohomology as well.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"26 1","pages":"291-352"},"PeriodicalIF":1.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78992078","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: 8
SO(n, n+1)-surface group representations and Higgs bundles SO(n, n+1)-表面群表示与希格斯束
IF 1.9 1区 数学
Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2020-01-01 DOI: 10.24033/ASENS.2454
Brian Collier
{"title":"SO(n, n+1)-surface group representations and Higgs bundles","authors":"Brian Collier","doi":"10.24033/ASENS.2454","DOIUrl":"https://doi.org/10.24033/ASENS.2454","url":null,"abstract":"","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"32 1","pages":"1561-1616"},"PeriodicalIF":1.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75018428","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: 6
A sharp Freiman type estimate for semisums in two and three dimensional Euclidean spaces 二维和三维欧几里得空间中半体的尖锐Freiman型估计
IF 1.9 1区 数学
Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2019-01-01 DOI: 10.24033/asens.2458
A. Figalli, David Jerison
{"title":"A sharp Freiman type estimate for semisums in two and three dimensional Euclidean spaces","authors":"A. Figalli, David Jerison","doi":"10.24033/asens.2458","DOIUrl":"https://doi.org/10.24033/asens.2458","url":null,"abstract":"Freiman's Theorem is a classical result in additive combinatorics concerning the approximate structure of sets of integers that contain a high proportion of their internal sums. As a consequence, one can deduce an estimate for sets of real numbers: If A ⊂ R and ∣∣ 1 2 (A+A) ∣∣− |A| |A|, then A is close to its convex hull. In this paper we prove a sharp form of the analogous result in dimensions 2 and 3.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"18 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80474214","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: 9
Quasi-projectivity of the moduli space of smooth kähler-Einstein fano manifolds 光滑kähler-Einstein范诺流形模空间的拟投影性
IF 1.9 1区 数学
Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2018-05-01 DOI: 10.24033/ASENS.2365
Chi Li, Chi Li, Xiaowei Wang, Chenyang Xu
{"title":"Quasi-projectivity of the moduli space of smooth kähler-Einstein fano manifolds","authors":"Chi Li, Chi Li, Xiaowei Wang, Chenyang Xu","doi":"10.24033/ASENS.2365","DOIUrl":"https://doi.org/10.24033/ASENS.2365","url":null,"abstract":"In this note, we prove that there is a canonical continuous Hermitian metric on the CM line bundle over the proper moduli space M of smoothable Kahler-Einstein Fano varieties. The curvature of this metric is the Weil-Petersson current, which exists as a positive (1,1)-current on M and extends the canonical Weil-Petersson current on the moduli space parametrizing smooth Kahler-Einstein Fano manifoldsM. As a consequence, we show that the CM line bundle is nef and big on M and its restriction on M is ample.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"46 1","pages":"739-772"},"PeriodicalIF":1.9,"publicationDate":"2018-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74852409","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
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