Pub Date : 2021-01-01DOI: 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}
Pub Date : 2021-01-01DOI: 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}
Pub Date : 2021-01-01DOI: 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}
Pub Date : 2021-01-01DOI: 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}
Pub Date : 2020-12-14DOI: 10.4310/mrl.2022.v29.n6.a10
A. Navas, M. Ponce
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.
{"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}
Pub Date : 2020-12-10DOI: 10.4310/mrl.2022.v29.n1.a8
Hannah R. Schwartz
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.
在这个简短的注释中，对于每个非零整数n，我们构造了一个4-流形，它包含一对光滑一致的球面，具有一个平方n的公共对偶，但没有将一个球面带到另一个球面的自同构。我们的例子，除了表明对偶的平方零假设在Gabai和Scheniederman-Teichner版本的4D灯泡定理中都是必要的之外，还有一个有趣的特征，那就是这对球体的Freedman-Quinn和Kervaire-Milnor不变量都消失了。该证明对Akbulut Matveyev和Auckly Kim Melvin Ruberman关于著名的马祖软木的结果进行了令人惊讶的应用。
{"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}
Pub Date : 2020-11-08DOI: 10.4310/mrl.2022.v29.n3.a5
Xiaoqi Huang, C. Sogge
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.
{"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}
Pub Date : 2020-10-23DOI: 10.4310/mrl.2022.v29.n6.a3
Tom Holt, Weiyi Zhang
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.
{"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}
Pub Date : 2020-10-23DOI: 10.4310/mrl.2022.v29.n6.a5
Jacek Jendrej, A. Lawrie
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.
{"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}
Pub Date : 2020-10-20DOI: 10.4310/mrl.2022.v29.n2.a4
Jan Gregorovivc, F. Meylan
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. Then 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.
{"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}
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