Pure and Applied Mathematics Quarterly最新文献

{"title":"The sharp Gevrey Kotake–Narasimhan theorem with an elementary proof","authors":"D. Tartakoff","doi":"10.4310/pamq.2022.v18.n2.a18","DOIUrl":"https://doi.org/10.4310/pamq.2022.v18.n2.a18","url":null,"abstract":"","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70525929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Vanishing theorem of Kohn–Rossi cohomology class and rigidity of Sasakian space form","authors":"D. Chang, Shun-Cheng Chang, Ting-Jung Kuo, Chien Lin","doi":"10.4310/pamq.2022.v18.n2.a3","DOIUrl":"https://doi.org/10.4310/pamq.2022.v18.n2.a3","url":null,"abstract":"","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":"55 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70525956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The road to GGP","authors":"B. Gross","doi":"10.4310/pamq.2022.v18.n5.a4","DOIUrl":"https://doi.org/10.4310/pamq.2022.v18.n5.a4","url":null,"abstract":"","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70526241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quasi-random graphs of given density and Ramsey numbers","authors":"Qizhong Lin, Yusheng Li","doi":"10.4310/pamq.2022.v18.n6.a9","DOIUrl":"https://doi.org/10.4310/pamq.2022.v18.n6.a9","url":null,"abstract":"","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70526293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The exponential map of the complexification of the group of analytic Hamiltonian diffeomorphisms","authors":"Reebhu Bhattacharyya, D. Burns, Ernesto Lupercio, A. Uribe","doi":"10.4310/pamq.2022.v18.n1.a2","DOIUrl":"https://doi.org/10.4310/pamq.2022.v18.n1.a2","url":null,"abstract":"","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":"23 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70525633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Differential of a period mapping at a singularity","authors":"Mark R. Green, P. Griffiths","doi":"10.4310/pamq.2022.v18.n4.a6","DOIUrl":"https://doi.org/10.4310/pamq.2022.v18.n4.a6","url":null,"abstract":"Period mappings, or equivalently variations of Hodge structure, have been used both to study families of algebraic varieties and as a subject in its own right. Among the aspects of a period mapping Φ that have received special attention are (i) singularities: the analysis of the behavior of Φ along a lower dimensional subvariety outside of which Φ is defined, and (ii) infinitesimal properties: the study of the geometry reflected in the differential of Φ. In this paper we will seek to combine these two. The local 1-parameter situation is given by a period mapping Φ : ∆∗ → ΓD where Γ is generated by the monodromy operator T . If T = TsTu is the Jordan decomposition into its semi-simple and unipotent factors where N is the nilpotent logarithm of T , our study will divide into two general areas: (1) N = 0, then Φ extends to Φ: ∆ → ΓD where the image Φ(0) gives a polarized Hodge structure having an action of Ts. Our general references for the topics discussed in this paper are [CM-SP], [G1], and [CKS]. The first one treats period mappings and variations of Hodge structure, the second discusses infinitesimal methods in Hodge theory, and the third is a basic reference for singularities of period mappings. We shall generally use the notations in [GGR]. 1 2 MARK GREEN AND PHILLIP GRIFFITHS (2) N 6= 0, in which case we will assume that Ts = I. It is conjectured [GGR] that Φ extends to a mapping to a torodial like completion where Φ(0) is a limiting mixed Hodge structure. In case (1) the objective is define a generalized differential δΦ that detects the first non-trivial part of the variation of Φ around Φ(0). Our results will give a geometric interpretation of this in several cases. A guiding question (informally stated) is: Let Φ: M→ ΓD be the period mapping for a KSBA moduli space of general type varieties. Let Mf ⊂ M be the subvariety of the canonical completion M corresponding to singular varieties around which the local monodromy of a smoothing is finite. Then there is an extension Φ :Mf → ΓD and one would like to define subvarieties of ΓD whose intersections with Φ(Mf ) define “special” subvarieties of Mf . 1 For such subvarieties one could like to be able to say something about their structure, e.g., their expected codimension and tangent space. In case (2) the question is somewhat different. Here the leading part of the differential is N, which gives rise to the nilpotent orbit that approximates Φ. The weight filtration for the limiting mixed Hodge structure defines a filtration on the differential and the successive quotients encode geometric information. One application is using versions of Torelli at the boundary to try to infer versions of Torelli in the interior. 1We will not formally define “special.” It could mean, e.g., points of Mf corresponding to varieties that have additional algebraic cycles or have a particular singularity type. 2Related to (2) is the computation and examples of δΦ for a family of mixed Hodge structures. The theory fo","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70525790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimization results for sphere maps","authors":"J. D'Angelo","doi":"10.4310/pamq.2022.v18.n2.a5","DOIUrl":"https://doi.org/10.4310/pamq.2022.v18.n2.a5","url":null,"abstract":"","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70525967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Classification of the nilradical of $k$-th Yau algebras arising from singularities","authors":"Naveed Hussain, S. Yau, Huaiqing Zuo","doi":"10.4310/pamq.2022.v18.n3.a2","DOIUrl":"https://doi.org/10.4310/pamq.2022.v18.n3.a2","url":null,"abstract":"","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70526089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"$3$-reconstructibility of rooted trees","authors":"A. Kostochka, M. Nahvi, D. West, Dara Zirlin","doi":"10.4310/pamq.2022.v18.n6.a7","DOIUrl":"https://doi.org/10.4310/pamq.2022.v18.n6.a7","url":null,"abstract":"A rooted tree is ℓ -reconstructible if it is determined by its multiset of rooted subtrees (with the same root) obtained by deleting ℓ vertices. We determine which rooted trees are ℓ -reconstructible for ℓ ≤ 3 and show how this can be used to study reconstructibility of unrooted trees.","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70526215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sup-norm estimates for $overline{partial}$","authors":"Dusty Grundmeier, Lars Simon, Berit Stensønes","doi":"10.4310/pamq.2022.v18.n2.a8","DOIUrl":"https://doi.org/10.4310/pamq.2022.v18.n2.a8","url":null,"abstract":"","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70526019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}