Nagoya Mathematical Journal最新文献

{"title":"BIRATIONAL GEOMETRY OF SEXTIC DOUBLE SOLIDS WITH A COMPOUND SINGULARITY","authors":"ERIK PAEMURRU","doi":"10.1017/nmj.2024.17","DOIUrl":"https://doi.org/10.1017/nmj.2024.17","url":null,"abstract":"Sextic double solids, double covers of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763024000175_inline2.png\"/> <jats:tex-math> $mathbb P^3$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> branched along a sextic surface, are the lowest degree Gorenstein terminal Fano 3-folds, hence are expected to behave very rigidly in terms of birational geometry. Smooth sextic double solids, and those which are <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763024000175_inline3.png\"/> <jats:tex-math> $mathbb Q$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-factorial with ordinary double points, are known to be birationally rigid. In this paper, we study sextic double solids with an isolated compound <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763024000175_inline4.png\"/> <jats:tex-math> $A_n$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> singularity. We prove a sharp bound <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763024000175_inline5.png\"/> <jats:tex-math> $n leq 8$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, describe models for each <jats:italic>n</jats:italic> explicitly, and prove that sextic double solids with <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763024000175_inline6.png\"/> <jats:tex-math> $n&gt; 3$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> are birationally nonrigid.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"207 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142268627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"SCHRÖDINGER PROPAGATOR ON WIENER AMALGAM SPACES IN THE FULL RANGE","authors":"GUOPING ZHAO, WEICHAO GUO","doi":"10.1017/nmj.2024.14","DOIUrl":"https://doi.org/10.1017/nmj.2024.14","url":null,"abstract":"Using the technique of Gabor analysis, we characterize the boundedness of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002776302400014X_inline1.png\"/> <jats:tex-math> $e^{iDelta }: W^{p_1,q_1}_mrightarrow W^{p_2,q_2}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> with modulation and translation operators, where <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002776302400014X_inline2.png\"/> and <jats:italic>m</jats:italic> is a <jats:italic>v</jats:italic>-moderate weight. The sharp exponents for the boundedness are also characterized in the case of power weight.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"7 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"CONSTANCY OF THE HILBERT–SAMUEL FUNCTION","authors":"VINCENT COSSART, OLIVIER PILTANT, BERND SCHOBER","doi":"10.1017/nmj.2024.13","DOIUrl":"https://doi.org/10.1017/nmj.2024.13","url":null,"abstract":"We prove a criterion for the constancy of the Hilbert–Samuel function for locally Noetherian schemes such that the local rings are excellent at every point. More precisely, we show that the Hilbert–Samuel function is locally constant on such a scheme if and only if the scheme is normally flat along its reduction and the reduction itself is regular. Regularity of the underlying reduced scheme is a significant new property.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"26 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141152397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"WHEN IS THE SILTING-DISCRETENESS INHERITED?","authors":"TAKUMA AIHARA, TAKAHIRO HONMA","doi":"10.1017/nmj.2024.8","DOIUrl":"https://doi.org/10.1017/nmj.2024.8","url":null,"abstract":"<p>We explore when the silting-discreteness is inherited. As a result, one obtains that taking idempotent truncations and homological epimorphisms of algebras transmit the silting-discreteness. We also study classification of silting-discrete simply-connected tensor algebras and silting-indiscrete self-injective Nakayama algebras. This paper contains two appendices; one states that every derived-discrete algebra is silting-discrete, and the other is about triangulated categories whose silting objects are tilting.</p>","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"59 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140566575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"SUBCOMPLEXES OF CERTAIN FREE RESOLUTIONS","authors":"MAYA BANKS, ALEKSANDRA SOBIESKA","doi":"10.1017/nmj.2024.7","DOIUrl":"https://doi.org/10.1017/nmj.2024.7","url":null,"abstract":"We invoke the Bernstein–Gel<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763024000072_inline1.png\" /> <jats:tex-math> $'$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>fand–Gel<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763024000072_inline2.png\" /> <jats:tex-math> $'$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>fand (BGG) correspondence to study subcomplexes of free resolutions given by two well-known complexes, the Koszul and the Eagon–Northcott. This approach provides a complete characterization of the ranks of free modules in a subcomplex in the Koszul case and imposes numerical restrictions in the Eagon–Northcott case.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"19 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140302662","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"TILTING COMPLEXES AND CODIMENSION FUNCTIONS OVER COMMUTATIVE NOETHERIAN RINGS","authors":"MICHAL HRBEK, TSUTOMU NAKAMURA, JAN ŠŤOVÍČEK","doi":"10.1017/nmj.2024.1","DOIUrl":"https://doi.org/10.1017/nmj.2024.1","url":null,"abstract":"In the derived category of a commutative noetherian ring, we explicitly construct a silting object associated with each sp-filtration of the Zariski spectrum satisfying the “slice” condition. Our new construction is based on local cohomology and it allows us to study when the silting object is tilting. For a ring admitting a dualizing complex, this occurs precisely when the sp-filtration arises from a codimension function on the spectrum. In the absence of a dualizing complex, the situation is more delicate and the tilting property is closely related to the condition that the ring is a homomorphic image of a Cohen–Macaulay ring. We also provide dual versions of our results in the cosilting case.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"69 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140150357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"NOTE ON THE THREE-DIMENSIONAL LOG CANONICAL ABUNDANCE IN CHARACTERISTIC","authors":"ZHENG XU","doi":"10.1017/nmj.2024.3","DOIUrl":"https://doi.org/10.1017/nmj.2024.3","url":null,"abstract":"In this paper, we prove the nonvanishing and some special cases of the abundance for log canonical threefold pairs over an algebraically closed field &lt;jats:italic&gt;k&lt;/jats:italic&gt; of characteristic &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763024000035_inline2.png\" /&gt; &lt;jats:tex-math&gt; $p&gt; 3$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;. More precisely, we prove that if &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763024000035_inline3.png\" /&gt; &lt;jats:tex-math&gt; $(X,B)$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; be a projective log canonical threefold pair over &lt;jats:italic&gt;k&lt;/jats:italic&gt; and &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763024000035_inline4.png\" /&gt; &lt;jats:tex-math&gt; $K_{X}+B$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; is pseudo-effective, then &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763024000035_inline5.png\" /&gt; &lt;jats:tex-math&gt; $kappa (K_{X}+B)geq 0$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;, and if &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763024000035_inline6.png\" /&gt; &lt;jats:tex-math&gt; $K_{X}+B$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; is nef and &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763024000035_inline7.png\" /&gt; &lt;jats:tex-math&gt; $kappa (K_{X}+B)geq 1$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;, then &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763024000035_inline8.png\" /&gt; &lt;jats:tex-math&gt; $K_{X}+B$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; is semi-ample. As applications, we show that the log canonical rings of projective log canonical threefold pairs over &lt;jats:italic&gt;k&lt;/jats:italic&gt; are finitely generated and the abundance holds when the nef dimension &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763024000035_inline9.png\" /&gt; &lt;jats:tex-math&gt; $n(K_{X}+B)leq 2$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; or when the Albanese map &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0027763024000035_inline10.png\" /&gt; &lt;jats:tex-math&gt; $a_{X}:Xto mathrm {Alb}(X)$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; is nontrivial. Moreo","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"49 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140002463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"COUNTING GEOMETRIC BRANCHES VIA THE FROBENIUS MAP AND F-NILPOTENT SINGULARITIES","authors":"HAILONG DAO, KYLE MADDOX, VAIBHAV PANDEY","doi":"10.1017/nmj.2024.4","DOIUrl":"https://doi.org/10.1017/nmj.2024.4","url":null,"abstract":"We give an explicit formula to count the number of geometric branches of a curve in positive characteristic using the theory of tight closure. This formula readily shows that the property of having a single geometric branch characterizes <jats:italic>F</jats:italic>-nilpotent curves. Further, we show that a reduced, local <jats:italic>F</jats:italic>-nilpotent ring has a single geometric branch; in particular, it is a domain. Finally, we study inequalities of Frobenius test exponents along purely inseparable ring extensions with applications to <jats:italic>F</jats:italic>-nilpotent affine semigroup rings.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"134 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140002926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A CALCULATION OF THE PERFECTOIDIZATION OF SEMIPERFECTOID RINGS","authors":"RYO ISHIZUKA","doi":"10.1017/nmj.2024.2","DOIUrl":"https://doi.org/10.1017/nmj.2024.2","url":null,"abstract":"We show that perfectoidization can be (almost) calculated by using <jats:italic>p</jats:italic>-root closure in certain cases, including the semiperfectoid case. To do this, we focus on the universality of perfectoidizations and uniform completions, as well as the <jats:italic>p</jats:italic>-root closed property of integral perfectoid rings. Through this calculation, we establish a connection between a classical closure operation “<jats:italic>p</jats:italic>-root closure” used by Roberts in mixed characteristic commutative algebra and a more recent concept of “perfectoidization” introduced by Bhatt and Scholze in their theory of prismatic cohomology.","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"99 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139946698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A HOMOMORPHISM BETWEEN BOTT–SAMELSON BIMODULES","authors":"NORIYUKI ABE","doi":"10.1017/nmj.2023.38","DOIUrl":"https://doi.org/10.1017/nmj.2023.38","url":null,"abstract":"<p>In the previous paper, we defined a new category which categorifies the Hecke algebra. This is a generalization of the theory of Soergel bimodules. To prove theorems, the existences of certain homomorphisms between Bott–Samelson bimodules are assumed. In this paper, we prove this assumption. We only assume the vanishing of certain two-colored quantum binomial coefficients.</p>","PeriodicalId":49785,"journal":{"name":"Nagoya Mathematical Journal","volume":"53 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139515375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}