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Diminished Fermat-type arrangements and unexpected curves 减少费马型排列和意想不到的曲线
arXiv: Algebraic Geometry Pub Date : 2020-03-05 DOI: 10.5802/CRMATH.77
J. Kabat, Beata Strycharz-Szemberg
{"title":"Diminished Fermat-type arrangements and unexpected curves","authors":"J. Kabat, Beata Strycharz-Szemberg","doi":"10.5802/CRMATH.77","DOIUrl":"https://doi.org/10.5802/CRMATH.77","url":null,"abstract":"The purpose of this note is to present and study a new series of the so-called unexpected curves. They enjoy a surprising property to the effect that their degree grows to infinity, whereas the multiplicity at a general fat point remains constant, equal $3$, which is the least possible number appearing as the multiplicity of an unexpected curve at its singular point. We show that additionally the BMSS dual curves inherits the same pattern of behaviour.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132161587","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
Two coniveau filtrations 两次交叉过滤
arXiv: Algebraic Geometry Pub Date : 2020-03-04 DOI: 10.1215/00127094-2021-0055
Olivier Benoist, J. C. Ottem
{"title":"Two coniveau filtrations","authors":"Olivier Benoist, J. C. Ottem","doi":"10.1215/00127094-2021-0055","DOIUrl":"https://doi.org/10.1215/00127094-2021-0055","url":null,"abstract":"A cohomology class of a smooth complex variety of dimension $n$ has coniveau $geq c$ if it vanishes in the complement of a closed subvariety of codimension $geq c$, and has strong coniveau $geq c$ if it comes by proper pushforward from the cohomology of a smooth variety of dimension $leq n-c$. We show that these two notions differ in general, both for integral classes on smooth projective varieties and for rational classes on smooth open varieties.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114516193","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: 12
Equivalence of Kuo and Thom quantities for analytic functions 解析函数的Kuo和Thom量的等价性
arXiv: Algebraic Geometry Pub Date : 2020-03-03 DOI: 10.3792/PJAA.97.004
K. Bekka, S. Koike
{"title":"Equivalence of Kuo and Thom quantities for analytic\u0000 functions","authors":"K. Bekka, S. Koike","doi":"10.3792/PJAA.97.004","DOIUrl":"https://doi.org/10.3792/PJAA.97.004","url":null,"abstract":"Sufficiency of jets is a very important notion introduced by Rene Thom in order to establish the structural stability theory. The criteria for some sufficiency of jets are known as the Kuo condition and Thom type inequality, which are defined using the Kuo quantity and Thom quantity. Therefore these quantities are meaningful. In this paper we show the equivalence of Kuo and Thom quantities. Then we apply this result to the relative conditions to a given closed set.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"154 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127281623","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
Local comparisons of homological and homotopical mixed Hodge polynomials 同调与同局部混合Hodge多项式的局部比较
arXiv: Algebraic Geometry Pub Date : 2020-03-01 DOI: 10.3792/pjaa.96.006
Shoji Yokura
{"title":"Local comparisons of homological and homotopical mixed Hodge polynomials","authors":"Shoji Yokura","doi":"10.3792/pjaa.96.006","DOIUrl":"https://doi.org/10.3792/pjaa.96.006","url":null,"abstract":"For a simply connected complex algebraic variey $X$, by the mixed Hodge structures $(W_{bullet}, F^{bullet})$ and $(tilde W_{bullet}, tilde F^{bullet})$ of the homology group $H_{*}(X;mathbb Q)$ and the homotopy groups $pi_{*}(X)otimes mathbb Q$ respectively, we have the following mixed Hodge polynomials $$MH_X(t,u,v):= sum_{k,p,q} operatorname{dim} Bigl ( Gr_{F^{bullet}}^{p} Gr^{W_{bullet}}_{p+q} H_k (X;mathbb C) Bigr) t^{k} u^{-p} v^{-q},$$ $$quad , , MH^{pi}_X(t,u,v):= sum_{k,p,q} operatorname{dim} Bigl (Gr_{tilde F^{bullet}}^{p} Gr^{tilde W_{bullet}}_{p+q} (pi_k(X) otimes mathbb C) Bigr ) t^ku^{-p} v^{-q},$$ which are respectively called emph{the homological mixed Hodge polynomial} and emph{the homotopical mixed Hodge polynomial}. In this paper we discuss some inequalities concerning these two mixed Hodge polynomials.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129034922","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: 4
EKOR strata on Shimura varieties with parahoric reduction 志村上的EKOR地层具有旁消减性
arXiv: Algebraic Geometry Pub Date : 2020-03-01 DOI: 10.25534/TUPRINTS-00011543
Jens Hesse
{"title":"EKOR strata on Shimura varieties with parahoric reduction","authors":"Jens Hesse","doi":"10.25534/TUPRINTS-00011543","DOIUrl":"https://doi.org/10.25534/TUPRINTS-00011543","url":null,"abstract":"We investigate the geometry of the special fiber of the integral model of a Shimura variety with parahoric level at a given prime place. To be more precise, we deal with the EKOR stratification which interpolates between the Ekedahl-Oort and Kottwitz-Rapoport stratifications. In the Siegel case we give a geometric description by suitably generalizing the theory of $G$-zips of Moonen, Wedhorn, Pink and Ziegler to our context.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126641644","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
Boundedness of log pluricanonical representationsof log Calabi–Yau pairs in dimension 2 2维对数Calabi-Yau对对数多范式表示的有界性
arXiv: Algebraic Geometry Pub Date : 2020-02-27 DOI: 10.2140/ANT.2021.15.547
Chen Jiang, Haidong Liu
{"title":"Boundedness of log pluricanonical representations\u0000of log Calabi–Yau pairs in dimension 2","authors":"Chen Jiang, Haidong Liu","doi":"10.2140/ANT.2021.15.547","DOIUrl":"https://doi.org/10.2140/ANT.2021.15.547","url":null,"abstract":"We show the boundedness of B-pluricanonical representations of lc log Calabi-Yau pairs in dimension $2$. As applications, we prove the boundedness of indices of slc log Calabi-Yau pairs up to dimension $3$ and that of non-klt lc log Calabi-Yau pairs in dimension $4$.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134044026","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
The Lang–Vojta Conjectures on Projective Pseudo-Hyperbolic Varieties 关于射影伪双曲变体的Lang-Vojta猜想
arXiv: Algebraic Geometry Pub Date : 2020-02-27 DOI: 10.1007/978-3-030-49864-1_3
A. Javanpeykar
{"title":"The Lang–Vojta Conjectures on Projective Pseudo-Hyperbolic Varieties","authors":"A. Javanpeykar","doi":"10.1007/978-3-030-49864-1_3","DOIUrl":"https://doi.org/10.1007/978-3-030-49864-1_3","url":null,"abstract":"","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123908555","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: 35
General elephants for threefold extremal contractions with one-dimensional fibers: exceptional case 一般大象用一维纤维进行三次极端收缩:例外情况
arXiv: Algebraic Geometry Pub Date : 2020-02-25 DOI: 10.1070/sm9388
Prokhorov Yuri, Mori Shigefumi
{"title":"General elephants for threefold extremal contractions with one-dimensional fibers: exceptional case","authors":"Prokhorov Yuri, Mori Shigefumi","doi":"10.1070/sm9388","DOIUrl":"https://doi.org/10.1070/sm9388","url":null,"abstract":"Let $(X, C)$ be a germ of a threefold $X$ with terminal singularities along a connected reduced complete curve $C$ with a contraction $f : (X, C) to (Z, o)$ such that $C = f^{-1} (o)_{mathrm{red}}$ and $-K_X$ is $f$-ample. Assume that each irreducible component of $C$ contains at most one point of index $>2$. We prove that a general member $Din |{-}K_X|$ is a normal surface with Du Val singularities.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"178 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116210506","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
Properties of the resolution of almost Gorenstein algebras 概Gorenstein代数的分解性质
arXiv: Algebraic Geometry Pub Date : 2020-02-17 DOI: 10.1016/J.JPAA.2021.106810
G. Zappala
{"title":"Properties of the resolution of almost Gorenstein algebras","authors":"G. Zappala","doi":"10.1016/J.JPAA.2021.106810","DOIUrl":"https://doi.org/10.1016/J.JPAA.2021.106810","url":null,"abstract":"","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"704 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"119560015","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
Very special algebraic groups 非常特殊的代数群
arXiv: Algebraic Geometry Pub Date : 2020-02-17 DOI: 10.5802/CRMATH.86
M. Brion, Emmanuel Peyre
{"title":"Very special algebraic groups","authors":"M. Brion, Emmanuel Peyre","doi":"10.5802/CRMATH.86","DOIUrl":"https://doi.org/10.5802/CRMATH.86","url":null,"abstract":"We say that a smooth algebraic group $G$ over a field $k$ is very special if for any field extension $K/k$, every $G_K$-homogeneous $K$-variety has a $K$-rational point. It is known that every split solvable linear algebraic group is very special. In this note, we show that the converse holds, and discuss its relationship with the birational classification of algebraic group actions.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123602386","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
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