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$4d$ $N=2$ SCFT and singularity theory Part IV: Isolated rational Gorenstein non-complete intersection singularities with at least one-dimensional deformation and nontrivial $T^2$ $4d$ N=2$ SCFT与奇点理论第四部分:具有至少一维变形和非平凡$T^2$的孤立有理Gorenstein非完全相交奇点
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2021-01-01 DOI: 10.4310/MRL.2021.V28.N1.A1
Bingyi Chen, S. Yau, S. Yau, Huaiqing Zuo
{"title":"$4d$ $N=2$ SCFT and singularity theory Part IV: Isolated rational Gorenstein non-complete intersection singularities with at least one-dimensional deformation and nontrivial $T^2$","authors":"Bingyi Chen, S. Yau, S. Yau, Huaiqing Zuo","doi":"10.4310/MRL.2021.V28.N1.A1","DOIUrl":"https://doi.org/10.4310/MRL.2021.V28.N1.A1","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":"70516435","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
Slope filtrations of $F$-isocrystals and logarithmic decay $F$-等晶的斜率过滤和对数衰减
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2021-01-01 DOI: 10.4310/MRL.2021.V28.N1.A5
Joe Kramer-Miller
{"title":"Slope filtrations of $F$-isocrystals and logarithmic decay","authors":"Joe Kramer-Miller","doi":"10.4310/MRL.2021.V28.N1.A5","DOIUrl":"https://doi.org/10.4310/MRL.2021.V28.N1.A5","url":null,"abstract":"","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"28 1","pages":"107-125"},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516498","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
On the existence of specialization isomorphisms of admissible fundamental groups in positive characteristic 论正特征上可容许基群的专门化同构的存在性
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2021-01-01 DOI: 10.4310/mrl.2021.v28.n6.a11
Yu Yang
{"title":"On the existence of specialization isomorphisms of admissible fundamental groups in positive characteristic","authors":"Yu Yang","doi":"10.4310/mrl.2021.v28.n6.a11","DOIUrl":"https://doi.org/10.4310/mrl.2021.v28.n6.a11","url":null,"abstract":"Let p be a prime number, and let Mg,n be the moduli stack over an algebraic closure Fp of the finite field Fp parameterizing pointed stable curves of type (g, n), Mg,n the open substack of Mg,n parameterizing smooth pointed stable curves, Mg,n the coarse moduli space of Mg,n, Mg,n the coarse moduli space of Mg,n, q ∈ Mg,n an arbitrary point, and Πq the admissible fundamental group of a pointed stable curve corresponding to a geometric point over q. In the present paper, we prove that, there exists q1, q2 ∈ Mg,n Mg,n such that q1 is a specialization of q2, that q1 ̸= q2, and that a specialization homomorphism sp : Πq2 ↠ Πq1 is an isomorphism.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"15 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516919","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
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
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
Extending vector bundles on curves 在曲线上扩展向量束
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2020-10-07 DOI: 10.4310/mrl.2022.v29.n5.a10
S. Mathur
{"title":"Extending vector bundles on curves","authors":"S. Mathur","doi":"10.4310/mrl.2022.v29.n5.a10","DOIUrl":"https://doi.org/10.4310/mrl.2022.v29.n5.a10","url":null,"abstract":"Given a curve in a (smooth) projective variety C subset X, we show that a vector bundle V on C can be extended to a (mu-stable) vector bundle on X if text{rank}(V) geq text{dim}(X) and text{det}(V) extends to X.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2020-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44152382","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
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