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Categorical dimension of birational transformations and filtrations of Cremona groups Cremona群的对偶变换和过滤的范畴维数
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2021-04-13 DOI: 10.2969/JMSJ/82658265
M. Bernardara
{"title":"Categorical dimension of birational transformations and filtrations of Cremona groups","authors":"M. Bernardara","doi":"10.2969/JMSJ/82658265","DOIUrl":"https://doi.org/10.2969/JMSJ/82658265","url":null,"abstract":"Using a filtration on the Grothendieck ring of triangulated categories, we define the motivic categorical dimension of a birational map between smooth projective varieties. We show that birational transformations of bounded motivic categorical dimension form subgroups, which provide a nontrivial filtration of the Cremona group. We discuss some geometrical aspect and some explicit example. We can moreover define, in some cases, the genus of a birational transformation, and compare it to the one defined by Frumkin in the case of threefolds.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47672938","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}
引用次数: 1
An asymptotic formula for the $2k$-th power mean value of $|(L^{prime}/L)(1+it_0, chi)|$ $|（L^｛prime｝/L）（1+it_0，chi）的$2k次幂均值的一个渐近公式|$
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2021-04-09 DOI: 10.2969/JMSJ/79987998
Kohji Matsumoto, S. S. Eddin
{"title":"An asymptotic formula for the $2k$-th power mean value of $|(L^{prime}/L)(1+it_0, chi)|$","authors":"Kohji Matsumoto, S. S. Eddin","doi":"10.2969/JMSJ/79987998","DOIUrl":"https://doi.org/10.2969/JMSJ/79987998","url":null,"abstract":"","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44189437","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}
引用次数: 0
On a density property of the residual order of $a pmod{pq}$ 关于$apmod｛pq｝剩余阶的密度性质$
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2021-04-01 DOI: 10.2969/JMSJ/82968296
L. Murata
{"title":"On a density property of the residual order of $a pmod{pq}$","authors":"L. Murata","doi":"10.2969/JMSJ/82968296","DOIUrl":"https://doi.org/10.2969/JMSJ/82968296","url":null,"abstract":"We consider a distribution property of the residual order (the multiplicative order) of the residue class $a hspace{-.4em} pmod{pq}$. It is known that the residual order fluctuates irregularly and increases quite rapidly. We are interested in how the residual orders $a hspace{-.4em} pmod{pq}$ distribute modulo 4 when we fix $a$ and let $p$ and $q$ vary. In this paper we consider the set $S(x) = {(p, q); p, q text{are distinct primes,} pq leq x }$, and calculate the natural density of the set ${(p, q) in S(x); text{the residual order of} a hspace{-.4em} pmod{pq} equiv l hspace{-.4em} pmod{4}}$. We show that, under a simple assumption on $a$, these densities are ${5/9,, 1/18,, 1/3,, 1/18 }$ for $l= {0, 1, 2, 3 }$, respectively. For $l = 1, 3$ we need Generalized Riemann Hypothesis.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":"-1 1","pages":"1-10"},"PeriodicalIF":0.7,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48048424","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}
引用次数: 0
Counting elliptic fibrations on K3 surfaces K3曲面上椭圆纤维的计数
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2021-02-18 DOI: 10.2969/jmsj/88178817
Dino Festi, Davide Cesare Veniani
{"title":"Counting elliptic fibrations on K3 surfaces","authors":"Dino Festi, Davide Cesare Veniani","doi":"10.2969/jmsj/88178817","DOIUrl":"https://doi.org/10.2969/jmsj/88178817","url":null,"abstract":"We solve the problem of counting jacobian elliptic fibrations on an arbitrary complex projective K3 surface up to automorphisms. We then illustrate our method with several explicit examples.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47131814","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}
引用次数: 3
Some sharp null-form type estimates for the Klein–Gordon equation Klein-Gordon方程的一些明显的零形式估计
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2021-02-05 DOI: 10.2969/jmsj/86418641
Jayson Cunanan, Shobu Shiraki
{"title":"Some sharp null-form type estimates for the Klein–Gordon equation","authors":"Jayson Cunanan, Shobu Shiraki","doi":"10.2969/jmsj/86418641","DOIUrl":"https://doi.org/10.2969/jmsj/86418641","url":null,"abstract":"We establish a sharp bilinear estimate for the Klein–Gordon propagator in the spirit of recent work of Beltran–Vega. Our approach is inspired by work in the setting of the wave equation due to Bez, Jeavons and Ozawa. As a consequence of our main bilinear estimate, we deduce several sharp estimates of null-form type and recover some sharp Strichartz estimates found by Quilodrán and Jeavons.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43664170","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}
引用次数: 0
Note on bi-exactness for creation operators on Fock spaces 关于Fock空间上创建算子的双精确性的注记
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2021-01-26 DOI: 10.2969/jmsj/86338633
K. Hasegawa, Yusuke Isono, T. Kanda
{"title":"Note on bi-exactness for creation operators on Fock spaces","authors":"K. Hasegawa, Yusuke Isono, T. Kanda","doi":"10.2969/jmsj/86338633","DOIUrl":"https://doi.org/10.2969/jmsj/86338633","url":null,"abstract":"In this note, we introduce and study a notion of bi-exactness for creation operators acting on full, symmetric and anti-symmetric Fock spaces. This is a generalization of our previous work, in which we studied the case of anti-symmetric Fock spaces. As a result, we obtain new examples of solid actions as well as new proofs for some known solid actions. We also study free wreath product groups in the same context.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41525704","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}
引用次数: 0
Calabi–Yau structure and Bargmann type transformation on the Cayley projective plane Cayley投影平面上的Calabi-Yau结构和Bargmann型变换
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2021-01-19 DOI: 10.2969/jmsj/86638663
Kurando Baba, Kenro Furutani
{"title":"Calabi–Yau structure and Bargmann type transformation on the Cayley projective plane","authors":"Kurando Baba, Kenro Furutani","doi":"10.2969/jmsj/86638663","DOIUrl":"https://doi.org/10.2969/jmsj/86638663","url":null,"abstract":"Our purposes are to show the existence of a Calabi-Yau structure on the punctured cotangent bundle T ∗ 0 (P 2 O) of the Cayley projective plane P O and to construct a Bargmann type transformation between the L2-space on P 2 O and a space of holomorphic functions on T ∗ 0 (P 2 O), which corresponds to the Fock space in the case of the original Bargmann transformation. A Kähler structure on T ∗ 0 (P 2 O) was shown by identifying it with a quadrics in the complex space C{0} and the natural symplectic form of the cotangent bundle T ∗ 0 (P 2 O) is expressed as a Kähler form. Our method to construct the transformation is the pairing of polarizations, one is the natural Lagrangian foliation given by the projection map q : T ∗ 0 (P 2 O) −→ P O and the positive complex polarization defined by the Kähler structure. The transformation gives a quantization of the geodesic flow in terms of one parameter group of elliptic Fourier integral operators whose canonical relations are defined by the graph of the geodesic flow action at each time. It turn out that for the Cayley projective plane the results are not same with other cases of the original Bargmann transformation for Euclidean space, spheres and other projective spaces.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46330968","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}
引用次数: 0
$C^{m}$ semialgebraic sections over the plane 平面上的$C^{m}$半代数截面
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2021-01-16 DOI: 10.2969/jmsj/86258625
C. Fefferman, Garving K. Luli
{"title":"$C^{m}$ semialgebraic sections over the plane","authors":"C. Fefferman, Garving K. Luli","doi":"10.2969/jmsj/86258625","DOIUrl":"https://doi.org/10.2969/jmsj/86258625","url":null,"abstract":"for polynomials P1, · · · , Pr, Q1, · · · , Qs on R . (We allow the cases r = 0 or s = 0.) A semialgebraic function φ : E → R is a function whose graph {(x, φ(x)) : x ∈ E} is a semialgebraic set. We define smoothness in terms of C and C loc. Here, C m ( R,R ) denotes the space of all R-valued functions on R whose derivatives up to order m are continuous and bounded on R. C loc ( R,R ) denotes the space of R-valued functions on R with continuous derivatives up to order m. If D = 1, we write C (R) and C loc (R ) in place of C ( R,R )","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43528747","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}
引用次数: 6
Varieties of minimal rational tangents of unbendable rational curves subordinate to contact structures 接触结构下不可展有理曲线的最小有理切线的多样性
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2021-01-14 DOI: 10.2969/JMSJ/85868586
Jun-Muk Hwang
{"title":"Varieties of minimal rational tangents of unbendable rational curves subordinate to contact structures","authors":"Jun-Muk Hwang","doi":"10.2969/JMSJ/85868586","DOIUrl":"https://doi.org/10.2969/JMSJ/85868586","url":null,"abstract":"A nonsingular rational curve $C$ in a complex manifold $X$ whose normal bundle is isomorphic to $${mathcal O}_{{mathbb P}^1}(1)^{oplus p} oplus {mathcal O}_{{mathbb P}^1}^{oplus q}$$ for some nonnegative integers $p$ and $q$ is called an unbendable rational curve on $X$. Associated with it is the variety of minimal rational tangents (VMRT) at a point $x in C,$ which is the germ of submanifolds ${mathcal C}^C_x subset {mathbb P} T_x X$ consisting of tangent directions of small deformations of $C$ fixing $x$. Assuming that there exists a distribution $D subset TX$ such that all small deformations of $C$ are tangent to $D$, one asks what kind of submanifolds of projective space can be realized as the VMRT ${mathcal C}^C_x subset {mathbb P} D_x$. When $D subset TX$ is a contact distribution, a well-known necessary condition is that ${mathcal C}_x^C$ should be Legendrian with respect to the induced contact structure on ${mathbb P} D_x$. We prove that this is also a sufficient condition: we construct a complex manifold $X$ with a contact structure $D subset TX$ and an unbendable rational curve $C subset X$ such that all small deformations of $C$ are tangent to $D$ and the VMRT ${mathcal C}^C_x subset {mathbb P} D_x$ at some point $xin C$ is projectively isomorphic to an arbitrarily given Legendrian submanifold. Our construction uses the geometry of contact lines on the Heisenberg group and a technical ingredient is the symplectic geometry of distributions the study of which has originated from geometric control theory.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43249400","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}
引用次数: 2
Stochastic integrals and Brownian motion on abstract nilpotent Lie groups 抽象幂零李群上的随机积分和布朗运动
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2021-01-12 DOI: 10.2969/jmsj/84678467
T. Melcher
{"title":"Stochastic integrals and Brownian motion on abstract nilpotent Lie groups","authors":"T. Melcher","doi":"10.2969/jmsj/84678467","DOIUrl":"https://doi.org/10.2969/jmsj/84678467","url":null,"abstract":"We construct a class of iterated stochastic integrals with respect to Brownian motion on an abstract Wiener space which allows for the definition of Brownian motions on a general class of infinite-dimensional nilpotent Lie groups based on abstract Wiener spaces. We then prove that a Cameron--Martin type quasi-invariance result holds for the associated heat kernel measures in the non-degenerate case, and give estimates on the associated Radon--Nikodym derivative. We also prove that a log Sobolev estimate holds in this setting.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43483804","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}
引用次数: 0
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