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Virtual counts on $operatorname{Quot}$ schemes and the higher rank local DT/PT correspondence 虚拟计数基于$operatorname{Quot}$方案和更高级别的本地DT/PT通信
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2021-01-01 DOI: 10.4310/mrl.2021.v28.n4.a2
S. Beentjes, Andrea T. Ricolfi
{"title":"Virtual counts on $operatorname{Quot}$ schemes and the higher rank local DT/PT correspondence","authors":"S. Beentjes, Andrea T. Ricolfi","doi":"10.4310/mrl.2021.v28.n4.a2","DOIUrl":"https://doi.org/10.4310/mrl.2021.v28.n4.a2","url":null,"abstract":"","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516800","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}
引用次数: 2
Gelfand-Tsetlin modules for $mathfrak{gl}(m vert n)$ $mathfrak{gl}(m vert n)$的Gelfand-Tsetlin模块
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2021-01-01 DOI: 10.4310/mrl.2021.v28.n5.a5
V. Futorny, V. Serganova, Jian Zhang
{"title":"Gelfand-Tsetlin modules for $mathfrak{gl}(m vert n)$","authors":"V. Futorny, V. Serganova, Jian Zhang","doi":"10.4310/mrl.2021.v28.n5.a5","DOIUrl":"https://doi.org/10.4310/mrl.2021.v28.n5.a5","url":null,"abstract":"","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516857","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}
引用次数: 0
Period integrals of vector bundle sections and tautological systems 向量束截面的周期积分与重言系统
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2021-01-01 DOI: 10.4310/MRL.2021.V28.N2.A4
An Huang, B. Lian, S. Yau, Chenglong Yu
{"title":"Period integrals of vector bundle sections and tautological systems","authors":"An Huang, B. Lian, S. Yau, Chenglong Yu","doi":"10.4310/MRL.2021.V28.N2.A4","DOIUrl":"https://doi.org/10.4310/MRL.2021.V28.N2.A4","url":null,"abstract":"","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"28 1","pages":"415-434"},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516637","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}
引用次数: 0
Holomorphic maps between closed $SU(ell, m)$-orbits in Grassmannian manifolds 格拉斯曼流形中$SU( well, m)$-轨道之间的全纯映射
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2021-01-01 DOI: 10.4310/MRL.2021.V28.N3.A6
Sung-Yeon Kim
{"title":"Holomorphic maps between closed $SU(ell, m)$-orbits in Grassmannian manifolds","authors":"Sung-Yeon Kim","doi":"10.4310/MRL.2021.V28.N3.A6","DOIUrl":"https://doi.org/10.4310/MRL.2021.V28.N3.A6","url":null,"abstract":"","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"28 1","pages":"729-783"},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516744","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}
引用次数: 0
On the projective derivative cocycle for circle diffeomorphisms 关于圆微分同胚的投影导数共循环
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2020-12-14 DOI: 10.4310/mrl.2022.v29.n6.a10
A. Navas, M. Ponce
{"title":"On the projective derivative cocycle for circle diffeomorphisms","authors":"A. Navas, M. Ponce","doi":"10.4310/mrl.2022.v29.n6.a10","DOIUrl":"https://doi.org/10.4310/mrl.2022.v29.n6.a10","url":null,"abstract":"We study the projective derivative as a cocycle of Mobius transformations over groups of circle diffeomorphisms. By computing precise expressions for this cocycle, we obtain several results about reducibility and almost reducibility to a cocycle of rotations. We also introduce an extension of this cocycle to the diagonal action on the 3-torus for which we generalize the previous results.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49475969","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}
引用次数: 1
Duals of non-zero square 非零平方的对偶
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2020-12-10 DOI: 10.4310/mrl.2022.v29.n1.a8
Hannah R. Schwartz
{"title":"Duals of non-zero square","authors":"Hannah R. Schwartz","doi":"10.4310/mrl.2022.v29.n1.a8","DOIUrl":"https://doi.org/10.4310/mrl.2022.v29.n1.a8","url":null,"abstract":"In this short note, for each non-zero integer n we construct a 4-manifold containing a smoothly concordant pair of spheres with a common dual of square n but no automorphism carrying one sphere to the other. Our examples, besides showing that the square zero assumption on the dual is necessary in both Gabai's and Scheniederman-Teichner's version of the 4D Light Bulb Theorem, have the interesting feature that both the Freedman-Quinn and Kervaire-Milnor invariant of the pair of spheres vanishes. The proof gives a surprising application of results due to Akbulut-Matveyev and Auckly-Kim-Melvin-Ruberman pertaining to the well-known Mazur cork.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44379171","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}
引用次数: 1
Quasimode and Strichartz estimates for time-dependent Schrödinger equations with singular potentials 奇异势含时Schrödinger方程的Quasimode和Strichartz估计
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2020-11-08 DOI: 10.4310/mrl.2022.v29.n3.a5
Xiaoqi Huang, C. Sogge
{"title":"Quasimode and Strichartz estimates for time-dependent Schrödinger equations with singular potentials","authors":"Xiaoqi Huang, C. Sogge","doi":"10.4310/mrl.2022.v29.n3.a5","DOIUrl":"https://doi.org/10.4310/mrl.2022.v29.n3.a5","url":null,"abstract":"We generalize the Strichartz estimates for Schrodinger operators on compact manifolds of Burq, Gerard and Tzvetkov [10] by allowing critically singular potentials $V$. Specifically, we show that their $1/p$--loss $L^p_tL^q_x(Itimes M)$-Strichartz estimates hold for $e^{-itH_V}$ when $H_V=-Delta_g+V(x)$ with $Vin L^{n/2}(M)$ if $nge3$ or $Vin L^{1+delta}(M)$, $delta>0$, if $n=2$, with $(p,q)$ being as in the Keel-Tao theorem and $Isubset {mathbb R}$ a bounded interval. We do this by formulating and proving new \"quasimode\" estimates for scaled dyadic unperturbed Schrodinger operators and taking advantage of the the fact that $1/q'-1/q=2/n$ for the endpoint Strichartz estimates when $(p,q)=(2,2n/(n-2))$. We also show that the universal quasimode estimates that we obtain are saturated on {em any} compact manifolds; however, we suggest that they may lend themselves to improved Strichartz estimates in certain geometries using recently developed \"Kakeya-Nikodym\" techniques developed to obtain improved eigenfunction estimates assuming, say, negative curvatures.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45327163","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}
引用次数: 6
Almost Kähler Kodaira–Spencer problem 几乎Kähler Kodaira–Spencer问题
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2020-10-23 DOI: 10.4310/mrl.2022.v29.n6.a3
Tom Holt, Weiyi Zhang
{"title":"Almost Kähler Kodaira–Spencer problem","authors":"Tom Holt, Weiyi Zhang","doi":"10.4310/mrl.2022.v29.n6.a3","DOIUrl":"https://doi.org/10.4310/mrl.2022.v29.n6.a3","url":null,"abstract":"We show that the almost complex Hodge number $h^{0,1}$ varies with different choices of almost Kahler metrics. This answers the almost Kahler version of a question of Kodaira and Spencer.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49644954","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}
引用次数: 11
Continuous time soliton resolution for two-bubble equivariant wave maps 双泡等变波图的连续时间孤子分辨率
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2020-10-23 DOI: 10.4310/mrl.2022.v29.n6.a5
Jacek Jendrej, A. Lawrie
{"title":"Continuous time soliton resolution for two-bubble equivariant wave maps","authors":"Jacek Jendrej, A. Lawrie","doi":"10.4310/mrl.2022.v29.n6.a5","DOIUrl":"https://doi.org/10.4310/mrl.2022.v29.n6.a5","url":null,"abstract":"We consider the energy-critical wave maps equation from 1+2 dimensional Minkowski space into the 2-sphere, in the equivariant case. We prove that if a wave map decomposes, along a sequence of times, into a superposition of at most two rescaled harmonic maps (bubbles) and radiation, then such a decomposition holds for continuous time. If the equivariance degree equals one or two, we deduce, as a consequence of sequential soliton resolution results of Cote, and Jia and Kenig, that any topologically trivial equivariant wave map with energy less than four times the energy of the bubble asymptotically decomposes into (at most two) bubbles and radiation.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"5 7","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41249155","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}
引用次数: 4
Construction of counterexamples to the 2–jet determination Chern–Moser Theorem in higher codimension 高余维双射流确定陈-莫泽定理反例的构造
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2020-10-20 DOI: 10.4310/mrl.2022.v29.n2.a4
Jan Gregorovivc, F. Meylan
{"title":"Construction of counterexamples to the 2–jet determination Chern–Moser Theorem in higher codimension","authors":"Jan Gregorovivc, F. Meylan","doi":"10.4310/mrl.2022.v29.n2.a4","DOIUrl":"https://doi.org/10.4310/mrl.2022.v29.n2.a4","url":null,"abstract":"We first construct a counterexample of a generic quadratic submanifold of codimension $5$ in $Bbb C^9$ which admits a real analytic infinitesimal CR automorphism with homogeneous polynomial coefficients of degree $4.$ This example also resolves a question in the Tanaka prolongation theory that was open for more than 50 years. \u0000Then we give sufficient conditions to generate more counterexamples to the $2-$jet determination Chern-Moser Theorem in higher codimension. In particular, we construct examples of generic quadratic submanifolds with jet determination of arbitrarily high order.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43487764","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}
引用次数: 7
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