We extend a locally nilpotent derivation $delta$ on a ring $B$ to $B$-modules $M$ and investigate the properties of such $B$-modules $M$. It turns out that the various geometric properties of the associated $G_a$-action on Spec $B$ can be reflected on the properties of $M$.
{"title":"Locally nilpotent derivations on modules","authors":"Mikiya Tanaka","doi":"10.1215/KJM/1248983033","DOIUrl":"https://doi.org/10.1215/KJM/1248983033","url":null,"abstract":"We extend a locally nilpotent derivation $delta$ on a ring $B$ to $B$-modules $M$ and investigate the properties of such $B$-modules $M$. It turns out that the various geometric properties of the associated $G_a$-action on Spec $B$ can be reflected on the properties of $M$.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"108 1","pages":"131-159"},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66087267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A shallow water approximation for water waves","authors":"T. Iguchi","doi":"10.1215/KJM/1248983028","DOIUrl":"https://doi.org/10.1215/KJM/1248983028","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"49 1","pages":"13-55"},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1248983028","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66087634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Asymptotic stability of small solitary waves to 1D nonlinear Schrödinger equations with potential","authors":"Tetsu Mizumachi","doi":"10.1215/KJM/1250271380","DOIUrl":"https://doi.org/10.1215/KJM/1250271380","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"48 1","pages":"471-497"},"PeriodicalIF":0.0,"publicationDate":"2008-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66088064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A result of R. Durrett, D. Iglehart and D. Miller states that Brownian meander is Brownian motion conditioned to stay positive for a unit of time, in the sense that it is the weak limit, as $x$ goes to $0$, of Brownian motion started at $x>0$ and conditioned to stay positive for a unit of time. We extend this limit theorem to the case of multidimensional Brownian motion conditioned to stay in a smooth convex cone.
R. Durrett, D. Iglehart和D. Miller的结果表明，布朗弯曲是布朗运动在单位时间内被限制为正的，从某种意义上说，它是弱极限，当$x$趋于$0$时，布朗运动从$x$开始，并被限制为在单位时间内保持正。我们将这个极限定理推广到条件为停留在光滑凸锥上的多维布朗运动。
{"title":"Brownian motion conditioned to stay in a cone","authors":"Rodolphe Garbit","doi":"10.1215/KJM/1260975039","DOIUrl":"https://doi.org/10.1215/KJM/1260975039","url":null,"abstract":"A result of R. Durrett, D. Iglehart and D. Miller states that Brownian meander is Brownian motion conditioned to stay positive for a unit of time, in the sense that it is the weak limit, as $x$ goes to $0$, of Brownian motion started at $x>0$ and conditioned to stay positive for a unit of time. We extend this limit theorem to the case of multidimensional Brownian motion conditioned to stay in a smooth convex cone.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"49 1","pages":"573-592"},"PeriodicalIF":0.0,"publicationDate":"2008-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66114019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On a generalization of Massey products","authors":"T. Mizuno","doi":"10.1215/KJM/1250271388","DOIUrl":"https://doi.org/10.1215/KJM/1250271388","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"27 1","pages":"639-659"},"PeriodicalIF":0.0,"publicationDate":"2008-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1250271388","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66088355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let $H$ be an ample line bundle on a non-singular projective surface $X$, and $M(H)$ the coarse moduli scheme of rank-two $H$-semistable sheaves with fixed Chern classes on $X$. We show that if $H$ changes and passes through walls to get closer to $K_X$, then $M(H)$ undergoes natural flips with respect to canonical divisors. When $X$ is minimal and its Kodaira dimension is positive, this sequence of flips terminates in $M(H_X)$; $H_X$ is an ample line bundle lying so closely to $K_X$ that the canonical divisor of $M(H_X)$ is nef. Remark that so-called Thaddeus-type flips somewhat differ from flips with respect to canonical divisors.
{"title":"Flips and variation of moduli scheme of sheaves on a surface","authors":"Kimiko Yamada","doi":"10.1215/KJM/1256219165","DOIUrl":"https://doi.org/10.1215/KJM/1256219165","url":null,"abstract":"Let $H$ be an ample line bundle on a non-singular projective surface $X$, and $M(H)$ the coarse moduli scheme of rank-two $H$-semistable sheaves with fixed Chern classes on $X$. We show that if $H$ changes and passes through walls to get closer to $K_X$, then $M(H)$ undergoes natural flips with respect to canonical divisors. When $X$ is minimal and its Kodaira dimension is positive, this sequence of flips terminates in $M(H_X)$; $H_X$ is an ample line bundle lying so closely to $K_X$ that the canonical divisor of $M(H_X)$ is nef. Remark that so-called Thaddeus-type flips somewhat differ from flips with respect to canonical divisors.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"49 1","pages":"419-425"},"PeriodicalIF":0.0,"publicationDate":"2008-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66113877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Faltings-Moriwaki modular height and isogenies of elliptic curves","authors":"H. Ikoma","doi":"10.1215/KJM/1250271389","DOIUrl":"https://doi.org/10.1215/KJM/1250271389","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"48 1","pages":"661-682"},"PeriodicalIF":0.0,"publicationDate":"2008-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66088371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
It is classical to approximate the distribution of fractional Brownian motion by a renormalized sum $ S_n $ of dependent Gaussian random variables. In this paper we consider such a walk $ Z_n $ that collects random rewards $ xi_j $ for $ j in mathbb Z,$ when the ceiling of the walk $ S_n $ is located at $ j.$ The random reward (or scenery) $ xi_j $ is independent of the walk and with heavy tail. We show the convergence of the sum of independent copies of $ Z_n$ suitably renormalized to a stable motion with integral representation, whose kernel is the local time of a fractional Brownian motion (fBm). This work extends a previous work where the random walk $ S_n$ had independent increments limits.
{"title":"Convergence of dependent walks in a random scenery to fBm-local time fractional stable motions","authors":"Serge Cohen, C. Dombry","doi":"10.1215/KJM/1256219156","DOIUrl":"https://doi.org/10.1215/KJM/1256219156","url":null,"abstract":"It is classical to approximate the distribution of fractional Brownian motion by a renormalized sum $ S_n $ of dependent Gaussian random variables. In this paper we consider such a walk $ Z_n $ that collects random rewards $ xi_j $ for $ j in mathbb Z,$ when the ceiling of the walk $ S_n $ is located at $ j.$ The random reward (or scenery) $ xi_j $ is independent of the walk and with heavy tail. We show the convergence of the sum of independent copies of $ Z_n$ suitably renormalized to a stable motion with integral representation, whose kernel is the local time of a fractional Brownian motion (fBm). This work extends a previous work where the random walk $ S_n$ had independent increments limits.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"49 1","pages":"267-286"},"PeriodicalIF":0.0,"publicationDate":"2008-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66113584","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The theta map sends code polynomials into the ring of Siegel modular forms of even weights. Explicit description of the image is known for g ≤ 3 and the surjectivity of the theta map follows. Instead it is known that this map is not surjective for g ≥ 5. In this paper we discuss the possibility of an embedding between the associated projective varieties. We prove that this is not possible for g ≥ 4 and consequently we get the non surjectivity of the graded rings for the remaining case g = 4.
{"title":"On the image of code polynomials under theta map","authors":"M. Oura, R. Manni","doi":"10.1215/KJM/1250271322","DOIUrl":"https://doi.org/10.1215/KJM/1250271322","url":null,"abstract":"The theta map sends code polynomials into the ring of Siegel modular forms of even weights. Explicit description of the image is known for g ≤ 3 and the surjectivity of the theta map follows. Instead it is known that this map is not surjective for g ≥ 5. In this paper we discuss the possibility of an embedding between the associated projective varieties. We prove that this is not possible for g ≥ 4 and consequently we get the non surjectivity of the graded rings for the remaining case g = 4.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"48 1","pages":"895-906"},"PeriodicalIF":0.0,"publicationDate":"2008-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66087931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the moduli spaces and compute the fundamental groups of plane sextics of torus type with at least two type E6 singular points. As a simple application, we compute the fundamental groups of 125 other sextics, most of which are new.
{"title":"Fundamental groups of symmetric sextics","authors":"A. Degtyarev","doi":"10.1215/KJM/1250271318","DOIUrl":"https://doi.org/10.1215/KJM/1250271318","url":null,"abstract":"We study the moduli spaces and compute the fundamental groups of plane sextics of torus type with at least two type E6 singular points. As a simple application, we compute the fundamental groups of 125 other sextics, most of which are new.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"48 1","pages":"765-792"},"PeriodicalIF":0.0,"publicationDate":"2008-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66087871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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