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Perverse Sheaves over Real Hyperplane Arrangements II 实超平面排列上的反常束2
IF 1.2 2区 数学
Publications of the Research Institute for Mathematical Sciences Pub Date : 2019-10-03 DOI: 10.4171/prims/58-4-5
M. Kapranov, V. Schechtman
{"title":"Perverse Sheaves over Real Hyperplane Arrangements II","authors":"M. Kapranov, V. Schechtman","doi":"10.4171/prims/58-4-5","DOIUrl":"https://doi.org/10.4171/prims/58-4-5","url":null,"abstract":"Let H be an arrangement of hyperplanes in R and PervpC,Hq be the category of perverse sheaves on C smooth with respect to the stratification given by complexified flats of H. We give a description of PervpC,Hq in terms of “matrix diagrams”, i.e., diagrams formed by vector spaces EA,B labelled by pairs pA,Bq of real faces of H (of all dimensions) or, equivalently, by the cells iA ` B of a natural cell decomposition of C. A matrix diagram is formally similar to a datum describing a constructible (non-perverse) sheaf but with the direction of one half of the arrows reversed.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43542553","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}
引用次数: 2
The Category $mathcal O$ for Lie Algebras of Vector Fields (I): Tilting Modules and Character Formulas 向量场李代数的范畴数学O (I):倾斜模和特征公式
IF 1.2 2区 数学
Publications of the Research Institute for Mathematical Sciences Pub Date : 2019-07-28 DOI: 10.4171/prims/56-4-3
Feifei Duan, B. Shu, Yufeng Yao
{"title":"The Category $mathcal O$ for Lie Algebras of Vector Fields (I): Tilting Modules and Character Formulas","authors":"Feifei Duan, B. Shu, Yufeng Yao","doi":"10.4171/prims/56-4-3","DOIUrl":"https://doi.org/10.4171/prims/56-4-3","url":null,"abstract":"In this article, we exploit the theory of graded module category with semi-infinite character developed by Soergel in cite{Soe} to study representations of the infinite dimensional Lie algebras of vector fields $W(n), S(n)$ and $H(n)$ $(ngeq 2)$, and obtain the description of indecomposable tilting modules. The character formulas for those tilting modules are determined.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/prims/56-4-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46201998","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}
引用次数: 1
Absolute Schauder Decompositions and Linearization of Holomorphic Mappings of Bounded Type 有界型全纯映射的绝对Schauder分解与线性化
IF 1.2 2区 数学
Publications of the Research Institute for Mathematical Sciences Pub Date : 2019-07-22 DOI: 10.4171/PRIMS/55-3-6
G. Botelho, V. V. Fávaro, J. Mujica
{"title":"Absolute Schauder Decompositions and Linearization of Holomorphic Mappings of Bounded Type","authors":"G. Botelho, V. V. Fávaro, J. Mujica","doi":"10.4171/PRIMS/55-3-6","DOIUrl":"https://doi.org/10.4171/PRIMS/55-3-6","url":null,"abstract":"","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/PRIMS/55-3-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48660351","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}
引用次数: 1
Groups of Extended Affine Lie Type 扩展仿射李型的群
IF 1.2 2区 数学
Publications of the Research Institute for Mathematical Sciences Pub Date : 2019-07-22 DOI: 10.4171/PRIMS/55-3-5
S. Azam, A. Parsa
{"title":"Groups of Extended Affine Lie Type","authors":"S. Azam, A. Parsa","doi":"10.4171/PRIMS/55-3-5","DOIUrl":"https://doi.org/10.4171/PRIMS/55-3-5","url":null,"abstract":"We construct certain Steinberg groups associated to extended affine Lie algebras and their root systems. Then by the integration methods of Kac and Peterson for integrable Lie algebras, we associate a group to every tame extended affine Lie algebra. Afterwards, we show that the extended affine Weyl group of the ground Lie algebra can be recovered as a quotient group of two subgroups of the group associated to the underlying algebra similar to Kac-Moody groups.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/PRIMS/55-3-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41321305","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}
引用次数: 3
Period Map of Triple Coverings of P$^2$ and Mixed Hodge Structures P$^2$三重复盖与混合Hodge结构的周期图
IF 1.2 2区 数学
Publications of the Research Institute for Mathematical Sciences Pub Date : 2019-07-22 DOI: 10.4171/PRIMS/55-3-2
Keiji Matsumoto, T. Terasoma
{"title":"Period Map of Triple Coverings of P$^2$ and Mixed Hodge Structures","authors":"Keiji Matsumoto, T. Terasoma","doi":"10.4171/PRIMS/55-3-2","DOIUrl":"https://doi.org/10.4171/PRIMS/55-3-2","url":null,"abstract":"","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/PRIMS/55-3-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47825372","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}
引用次数: 1
Cograde Conditions and Cotorsion Pairs Cotrade条件和Cotorsion对
IF 1.2 2区 数学
Publications of the Research Institute for Mathematical Sciences Pub Date : 2019-07-12 DOI: 10.4171/prims/56-3-2
Xi Tang, Zhaoyong Huang
{"title":"Cograde Conditions and Cotorsion Pairs","authors":"Xi Tang, Zhaoyong Huang","doi":"10.4171/prims/56-3-2","DOIUrl":"https://doi.org/10.4171/prims/56-3-2","url":null,"abstract":"Let $R$ and $S$ be rings and $_Romega_S$ a semidualizing bimodule. We study when the double functor $Tor^S_i(omega, Ext^i_{R}(omega,-))$ preserves epimorphisms and the double functor $Ext_{R}^i(omega, Tor_i^{S}(omega,-))$ preserves monomorphisms in terms of the (strong) cograde conditions of modules. Under certain cograde condition of modules, we construct two complete cotorsion pairs. In addition, we establish the relation between some relative finitistic dimensions of rings and the right and left projective dimensions of $omega$.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47593947","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}
引用次数: 0
On Uniform K-Stability for Some Asymptotically log del Pezzo Surfaces 一类渐近log del Pezzo曲面的一致K稳定性
IF 1.2 2区 数学
Publications of the Research Institute for Mathematical Sciences Pub Date : 2019-07-11 DOI: 10.4171/prims/58-1-6
Kento Fujita
{"title":"On Uniform K-Stability for Some Asymptotically log del Pezzo Surfaces","authors":"Kento Fujita","doi":"10.4171/prims/58-1-6","DOIUrl":"https://doi.org/10.4171/prims/58-1-6","url":null,"abstract":"Motivated by the problem for the existence of Kahler-Einstein edge metrics, Cheltsov and Rubinstein conjectured the K-polystability of asymptotically log Fano varieties with small cone angles when the anti-log-canonical divisors are not big. Cheltsov, Rubinstein and Zhang proved it affirmatively in dimension $2$ with irreducible boundaries except for the type $(operatorname{I.9B.}n)$ with $1leq nleq 6$. Unfortunately, recently, Fujita, Liu, Suss, Zhang and Zhuang showed the non-K-polystability for some members of type $(operatorname{I.9B.}1)$ and for some members of type $(operatorname{I.9B.}2)$. In this article, we show that Cheltsov--Rubinstein's problem is true for all of the remaining cases. More precisely, we explicitly compute the delta-invariant for asymptotically log del Pezzo surfaces of type $(operatorname{I.9B.}n)$ for all $ngeq 1$ with small cone angles. As a consequence, we finish Cheltsov--Rubinstein's problem in dimension $2$ with irreducible boundaries.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47522358","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}
引用次数: 4
Characterizing the Increase of the Residual Order under Blowup in Positive Characteristic 正特性爆破下残差阶增加的表征
IF 1.2 2区 数学
Publications of the Research Institute for Mathematical Sciences Pub Date : 2019-06-23 DOI: 10.4171/prims/55-4-7
H. Hauser, Stefan Perlega
{"title":"Characterizing the Increase of the Residual Order under Blowup in Positive Characteristic","authors":"H. Hauser, Stefan Perlega","doi":"10.4171/prims/55-4-7","DOIUrl":"https://doi.org/10.4171/prims/55-4-7","url":null,"abstract":"In characteristic zero, the residual order constitutes, after the local multiplicity, the second key invariant for the resolution of singularities. It is defined as the order of the coefficient ideal in a local hypersurface of maximal contact, minus the exceptional multiplicities. It does not increase under blowup in permissible centers as long as the local multiplicity remains constant. In positive characteristic, however, the residual order (defined now as the maximum over all smooth local hypersurfaces) may increase under blowup. In the article we analyze in detail the circumstances when this happens. This may help to develop a modification of the residual order which does work in positive characteristic.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/prims/55-4-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44771384","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}
引用次数: 3
On the Existence of Minimal Models for Log Canonical Pairs 关于对数正则对最小模型的存在性
IF 1.2 2区 数学
Publications of the Research Institute for Mathematical Sciences Pub Date : 2019-05-14 DOI: 10.4171/PRIMS/58-2-3
Vladimir Lazi'c, Nikolaos Tsakanikas
{"title":"On the Existence of Minimal Models for Log Canonical Pairs","authors":"Vladimir Lazi'c, Nikolaos Tsakanikas","doi":"10.4171/PRIMS/58-2-3","DOIUrl":"https://doi.org/10.4171/PRIMS/58-2-3","url":null,"abstract":"We show that minimal models of log canonical pairs exist, assuming the existence of minimal models of smooth varieties.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41481660","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}
引用次数: 18
The Semi-absolute Anabelian Geometry of Geometrically Pro-$p$ Arithmetic Fundamental Groups of Associated Low-Dimensional Configuration Spaces 相关低维位形空间的几何亲p算术基本群的半绝对可逆几何
IF 1.2 2区 数学
Publications of the Research Institute for Mathematical Sciences Pub Date : 2019-03-25 DOI: 10.14989/DOCTOR.K21544
Kazumi Higashiyama
{"title":"The Semi-absolute Anabelian Geometry of Geometrically Pro-$p$ Arithmetic Fundamental Groups of Associated Low-Dimensional Configuration Spaces","authors":"Kazumi Higashiyama","doi":"10.14989/DOCTOR.K21544","DOIUrl":"https://doi.org/10.14989/DOCTOR.K21544","url":null,"abstract":"Let p be a prime number. In the present paper, we study geometrically pro-p arithmetic fundamental groups of low-dimensional configuration spaces associated to a given hyperbolic curve over an arithmetic field such as a number field or a p-adic local field. Our main results concern the group-theoretic reconstruction of the function field of certain tripods (i.e., copies of the projective line minus three points) that lie inside such a configuration space from the associated geometrically pro-p arithmetic fundamental group, equipped with the auxiliary data constituted by the collection of decomposition groups determined by the closed points of the associated compactified configuration space. 2010 Mathematics Subject Classification: Primary 14H30; Secondary 14H10.","PeriodicalId":54528,"journal":{"name":"Publications of the Research Institute for Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2019-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43434915","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}
引用次数: 1
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