发布求助
文献互助 智能选刊 最新文献

Journal of Singularities最新文献

筛选
英文 中文
A generalization of Zakalyukin's lemma, and symmetries of surface singularities Zakalyukin引理的推广及曲面奇点的对称性
IF 0.4
Journal of Singularities Pub Date : 2021-04-08 DOI: 10.5427/jsing.2022.25m
Atsufumi Honda, K. Naokawa, K. Saji, M. Umehara, Kotaro Yamada
{"title":"A generalization of Zakalyukin's lemma, and symmetries of surface singularities","authors":"Atsufumi Honda, K. Naokawa, K. Saji, M. Umehara, Kotaro Yamada","doi":"10.5427/jsing.2022.25m","DOIUrl":"https://doi.org/10.5427/jsing.2022.25m","url":null,"abstract":"Zakalyukin’s lemma asserts that the coincidence of the images of two wave front germs implies the right equivalence of corresponding map germs under a certain genericity assumption. The purpose of this paper is to give an improvement of this lemma for frontals. Moreover, we give several applications for singularities on surfaces.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"96 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76703340","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}
引用次数: 1
Algebraic differential equations of period-integrals 周期积分的代数微分方程
IF 0.4
Journal of Singularities Pub Date : 2021-01-25 DOI: 10.5427/jsing.2022.25c
D. Barlet
{"title":"Algebraic differential equations of period-integrals","authors":"D. Barlet","doi":"10.5427/jsing.2022.25c","DOIUrl":"https://doi.org/10.5427/jsing.2022.25c","url":null,"abstract":"We explain that in the study of the asymptotic expansion at the origin of a period integral like ∫ γz ω/df or of a hermitian period like ∫ f=s ρ.ω/df ∧ ω′/df the computation of the Bernstein polynomial of the ”fresco” (filtered differential equation) associated to the pair of germs (f, ω) gives a better control than the computation of the Bernstein polynomial of the full Brieskorn module of the germ of f at the origin. Moreover, it is easier to compute as it has a better functoriality and smaller degree. We illustrate this in the case where f ∈ C[x0, . . . , xn] has n+ 2 monomials and is not quasi-homogeneous, by giving an explicite simple algorithm to produce a multiple of the Bernstein polynomial when ω is a monomial holomorphic volume form. Several concrete examples are given. AMS Classification. 32 S 2532 S 40","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"33 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74621931","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}
引用次数: 2
Linear isoperimetric inequality for normal and integral currents in compact subanalytic sets 紧亚解析集中正规电流和积分电流的线性等周不等式
IF 0.4
Journal of Singularities Pub Date : 2020-12-04 DOI: 10.5427/jsing.2022.24f
T. Pauw, R. Hardt
{"title":"Linear isoperimetric inequality for normal and integral currents in compact subanalytic sets","authors":"T. Pauw, R. Hardt","doi":"10.5427/jsing.2022.24f","DOIUrl":"https://doi.org/10.5427/jsing.2022.24f","url":null,"abstract":"The isoperimetric inequality for a smooth compact Riemannian manifold $A$ provides a positive ${bf c}(A)$, so that for any $k+1$ dimensional integral current $S_0$ in $A$ there exists an integral current $ S$ in $A$ with $partial S=partial S_0$ and ${bf M}(S)leq {bf c}(A){bf M}(partial S)^{(k+1)/k}$. Although such an inequality still holds for any compact Lipschitz neighborhood retract $A$, it may fail in case $A$ contains a single polynomial singularity. Here, replacing $(k+1)/k$ by $1$, we find that a linear inequality ${bf M}(S)leq {bf c}(A){bf M}(partial S)$ is valid for any compact algebraic, semi-algebraic, or even subanalytic set $A$. In such a set, this linear inequality holds not only for integral currents, which have $boldsymbol{Z}$ coefficients, but also for normal currents having $boldsymbol{R}$ coefficients and generally for normal flat chains with coefficients in any complete normed abelian group. A relative version for a subanalytic pair $Bsubset A$ is also true, and there are applications to variational and metric properties of subanalytic sets.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88302835","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}
引用次数: 3
Derived KZ Equations 导出的KZ方程
IF 0.4
Journal of Singularities Pub Date : 2020-12-04 DOI: 10.5427/jsing.2022.25u
V. Schechtman, A. Varchenko
{"title":"Derived KZ Equations","authors":"V. Schechtman, A. Varchenko","doi":"10.5427/jsing.2022.25u","DOIUrl":"https://doi.org/10.5427/jsing.2022.25u","url":null,"abstract":"In this paper we strengthen the results of [SV] by presenting their derived version. Namely, we define a \"derived Knizhnik - Zamolodchikov connection\" and identify it with a \"derived Gauss - Manin connection\".","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83060690","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}
引用次数: 2
Characteristic Classes of Homogeneous Essential Isolated Determinantal Varieties 齐次本质分离行列式变种的特征类
IF 0.4
Journal of Singularities Pub Date : 2020-11-25 DOI: 10.5427/jsing.2022.25w
Xiping Zhang
{"title":"Characteristic Classes of Homogeneous Essential Isolated Determinantal Varieties","authors":"Xiping Zhang","doi":"10.5427/jsing.2022.25w","DOIUrl":"https://doi.org/10.5427/jsing.2022.25w","url":null,"abstract":"The (homogeneous) Essentially Isolated Determinantal Variety is the natural generalization of generic determinantal variety, and is fundamental example to study non-isolated singularities. In this paper we study the characteristic classes on these varieties. We give explicit formulas of their Chern-Schwartz-MacPherson classes via standard Schubert calculus. As corollaries we obtain formulas for their (generic) sectional Euler characteristics, characteristic cycles and polar classes. In particular, when such variety is a hypersurfaces we compute its Milnor class and the Euler characteristics of the local Milnor fibers. We prove that for such recursive group orbit hypersurfaces the local Euler obstructions completely determine the Milnor classes. \u0000In general for reflective group orbits, on the other hand we propose an algorithm to compute their local Euler obstructions via the Chern-Schwartz-MacPherson classes of the orbits, which can be obtained directly from representation theory. This builds a bridge from representation theory of the group action to the singularity theory of the induced orbits.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"1994 11","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72400793","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}
引用次数: 1
Orbifold splice quotients and log covers of surface pairs 曲面对的轨道拼接商和对数覆盖
IF 0.4
Journal of Singularities Pub Date : 2020-11-18 DOI: 10.5427/jsing.2021.23i
W. Neumann, J. Wahl
{"title":"Orbifold splice quotients and log covers of surface pairs","authors":"W. Neumann, J. Wahl","doi":"10.5427/jsing.2021.23i","DOIUrl":"https://doi.org/10.5427/jsing.2021.23i","url":null,"abstract":"A three-dimensional orbifold $(Sigma, gamma_i, n_i)$, where $Sigma$ is a rational homology sphere, has a universal abelian orbifold covering, whose covering group is the first orbifold homology. A singular pair $(X,C)$, where $X$ is a normal surface singularity with $mathbb Q$HS link and $C$ is a Weil divisor, gives rise on its boundary to an orbifold. One studies the preceding orbifold notions in the algebro-geometric setting, in particular defining the universal abelian log cover of a pair. A first key theorem computes the orbifold homology from an appropriate resolution of the pair. In analogy with the case where $C$ is empty and one considers the universal abelian cover, under certain conditions on a resolution graph one can construct pairs and their universal abelian log covers. Such pairs are called orbifold splice quotients.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"53 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90755791","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}
引用次数: 0
What is the degree of a smooth hypersurface? 光滑超曲面的度是多少?
IF 0.4
Journal of Singularities Pub Date : 2020-10-27 DOI: 10.5427/jsing.2021.23l
A. Lerário, Michele Stecconi
{"title":"What is the degree of a smooth hypersurface?","authors":"A. Lerário, Michele Stecconi","doi":"10.5427/jsing.2021.23l","DOIUrl":"https://doi.org/10.5427/jsing.2021.23l","url":null,"abstract":"Let $D$ be a disk in $mathbb{R}^n$ and $fin C^{r+2}(D, mathbb{R}^k)$. We deal with the problem of the algebraic approximation of the set $j^{r}f^{-1}(W)$ consisting of the set of points in the disk $D$ where the $r$-th jet extension of $f$ meets a given semialgebraic set $Wsubset J^{r}(D, mathbb{R}^k).$ Examples of sets arising in this way are the zero set of $f$, or the set of its critical points. \u0000Under some transversality conditions, we prove that $f$ can be approximated with a polynomial map $p:Dto mathbb{R}^k$ such that the corresponding singularity is diffeomorphic to the original one, and such that the degree of this polynomial map can be controlled by the $C^{r+2}$ data of $f$. More precisely, begin{equation} text{deg}(p)le Oleft(frac{|f|_{C^{r+2}(D, mathbb{R}^k)}}{mathrm{dist}_{C^{r+1}}(f, Delta_W)}right), end{equation} \u0000where $Delta_W$ is the set of maps whose $r$-th jet extension is not transverse to $W$. The estimate on the degree of $p$ implies an estimate on the Betti numbers of the singularity, however, using more refined tools, we prove independently a similar estimate, but involving only the $C^{r+1}$ data of $f$. \u0000These results specialize to the case of zero sets of $fin C^{2}(D, mathbb{R})$, and give a way to approximate a smooth hypersurface defined by the equation $f=0$ with an algebraic one, with controlled degree (from which the title of the paper). In particular, we show that a compact hypersurface $Zsubset Dsubset mathbb{R}^n$ with positive reach $rho(Z)>0$ is isotopic to the zero set in $D$ of a polynomial $p$ of degree begin{equation} text{deg}(p)leq c(D)cdot 2 left(1+frac{1}{rho(Z)}+frac{5n}{rho(Z)^2}right),end{equation} where $c(D)>0$ is a constant depending on the size of the disk $D$ (and in particular on the diameter of $Z$).","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"128 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88342269","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}
引用次数: 3
On families of Lagrangian submanifolds 关于拉格朗日子流形的族
IF 0.4
Journal of Singularities Pub Date : 2020-10-22 DOI: 10.5427/jsing.2020.21j
S. Izumiya, Masatomo Takahashi
{"title":"On families of Lagrangian submanifolds","authors":"S. Izumiya, Masatomo Takahashi","doi":"10.5427/jsing.2020.21j","DOIUrl":"https://doi.org/10.5427/jsing.2020.21j","url":null,"abstract":"","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"11 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84195655","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}
引用次数: 0
On the growth behaviour of Hironaka quotients 关于Hironaka商的增长行为
IF 0.4
Journal of Singularities Pub Date : 2020-10-22 DOI: 10.5427/jsing.2020.21o
Junki Tanaka, T. Ohmoto
{"title":"On the growth behaviour of Hironaka quotients","authors":"Junki Tanaka, T. Ohmoto","doi":"10.5427/jsing.2020.21o","DOIUrl":"https://doi.org/10.5427/jsing.2020.21o","url":null,"abstract":"","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"3 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88162881","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}
引用次数: 0
Weighted homogeneous surface singularities homeomorphic to Brieskorn complete intersections Brieskorn完全交点的加权齐次曲面奇异同胚
IF 0.4
Journal of Singularities Pub Date : 2020-10-18 DOI: 10.5427/jsing.2021.23j
Tomohiro Okuma
{"title":"Weighted homogeneous surface singularities homeomorphic to Brieskorn complete intersections","authors":"Tomohiro Okuma","doi":"10.5427/jsing.2021.23j","DOIUrl":"https://doi.org/10.5427/jsing.2021.23j","url":null,"abstract":"For a given topological type of a normal surface singularity, there are various types of complex structures which realize it. We are interested in the following problem: Find the maximum of the geometric genus and a condition for that the maximal ideal cycle coincides with the undamental cycle on the minimal good resolution. In this paper, we study weighted homogeneous surface singularities homeomorphic to Brieskorn complete intersection singularities from the perspective of the problem.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":"3 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88093169","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}
引用次数: 0
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信