In this article, we give a simple proof of the comparison of nearby and vanishing cycles in the sense of Riemann-Hilbert correspondence following the idea of Beilinson and Bernstein, without using the Kashiwara-Malgrange $V$-filtrations.
{"title":"On the comparison of nearby cycles via b-functions","authors":"Lei Wu","doi":"10.5427/JSING.2021.23E","DOIUrl":"https://doi.org/10.5427/JSING.2021.23E","url":null,"abstract":"In this article, we give a simple proof of the comparison of nearby and vanishing cycles in the sense of Riemann-Hilbert correspondence following the idea of Beilinson and Bernstein, without using the Kashiwara-Malgrange $V$-filtrations.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131071268","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}
In this paper we classify varieties of Picard number two having two projective bundle structures of any relative dimension, under the assumption that these structures are mutually uniform. As an application we prove the Campana--Peternell conjecture for varieties of Picard number one admitting $mathbb C^*$-actions of a certain kind.
{"title":"Manifolds with two projective bundles structures","authors":"Gianluca Occhetta, Luis E. Sol'a Conde, E. Romano","doi":"10.1090/proc/15762","DOIUrl":"https://doi.org/10.1090/proc/15762","url":null,"abstract":"In this paper we classify varieties of Picard number two having two projective bundle structures of any relative dimension, under the assumption that these structures are mutually uniform. As an application we prove the Campana--Peternell conjecture for varieties of Picard number one admitting $mathbb C^*$-actions of a certain kind.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122639430","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}
Pub Date : 2020-01-14DOI: 10.2140/tunis.2021.3.571
M. Kashiwara, P. Schapira
On a complex symplectic manifold we prove a finiteness result for the global sections of solutions of holonomic DQ-modules in two cases: (a) by assuming that there exists a Poisson compactification (b) in the algebraic case. This extends our previous results in which the symplectic manifold was compact. The main tool is a finiteness theorem for R-constructible sheaves on a real analytic manifold in a non proper situation.
{"title":"A finiteness theorem for holonomic DQ-modules on Poisson manifolds","authors":"M. Kashiwara, P. Schapira","doi":"10.2140/tunis.2021.3.571","DOIUrl":"https://doi.org/10.2140/tunis.2021.3.571","url":null,"abstract":"On a complex symplectic manifold we prove a finiteness result for the global sections of solutions of holonomic DQ-modules in two cases: (a) by assuming that there exists a Poisson compactification (b) in the algebraic case. This extends our previous results in which the symplectic manifold was compact. The main tool is a finiteness theorem for R-constructible sheaves on a real analytic manifold in a non proper situation.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133720376","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}
Pub Date : 2020-01-11DOI: 10.1142/S0129167X21500270
R. Karmakar
Let $X = mathbb{P}(E_1) times_C mathbb{P}(E_2)$ where $C$ is a smooth curve and $E_1$, $E_2$ are vector bundles over $C$.In this paper we compute the pseudo effective cones of higher codimension cycles on $X$.
{"title":"Effective cones of cycles on products of projective bundles over curves","authors":"R. Karmakar","doi":"10.1142/S0129167X21500270","DOIUrl":"https://doi.org/10.1142/S0129167X21500270","url":null,"abstract":"Let $X = mathbb{P}(E_1) times_C mathbb{P}(E_2)$ where $C$ is a smooth curve and $E_1$, $E_2$ are vector bundles over $C$.In this paper we compute the pseudo effective cones of higher codimension cycles on $X$.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116463756","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}
Pub Date : 2019-12-28DOI: 10.17185/DUEPUBLICO/70523
Felix Gora
In this thesis we will analyse singularities of local models. More precisely we will attack the question of existence of semi-stable resolutions. We will discuss an approach mentioned in [Gen00]. In this approach a candidate for a semi-stable resolution was given as the blow-up of a Grassmannian variety in Schubert varieties of its special fiber. Explicit calculations with Sage described in Appendix D show that this approach is not working in general. Starting from the proof of flatness of the local models in [Gor01], we describe these local models as Mustafinvarieties over Grassmannian varieties. We are combining several results on the structure of Mustafin varieties over projective spaces (cf. [CHSW11],[AL17]) with the Plucker embedding to be able to construct a candidate for a semi-stable resolution of local models. Under some additional assumptions this candidate is generalising the approach suggested by Genestier. Furthermore under the same assumptions the new candidate agrees with the semi-stable resolution constructed in [Gor04] for small dimensions.
{"title":"Local models, Mustafin varieties and semi-stable resolutions","authors":"Felix Gora","doi":"10.17185/DUEPUBLICO/70523","DOIUrl":"https://doi.org/10.17185/DUEPUBLICO/70523","url":null,"abstract":"In this thesis we will analyse singularities of local models. More precisely we will attack the question of existence of semi-stable resolutions. We will discuss an approach mentioned in [Gen00]. In this approach a candidate for a semi-stable resolution was given as the blow-up of a Grassmannian variety in Schubert varieties of its special fiber. Explicit calculations with Sage described in Appendix D show that this approach is not working in general. Starting from the proof of flatness of the local models in [Gor01], we describe these local models as Mustafinvarieties over Grassmannian varieties. We are combining several results on the structure of Mustafin varieties over projective spaces (cf. [CHSW11],[AL17]) with the Plucker embedding to be able to construct a candidate for a semi-stable resolution of local models. Under some additional assumptions this candidate is generalising the approach suggested by Genestier. Furthermore under the same assumptions the new candidate agrees with the semi-stable resolution constructed in [Gor04] for small dimensions.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128200229","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}
Pub Date : 2019-12-20DOI: 10.2140/tunis.2021.3.469
G. Geer, E. Looijenga
The moduli space of principally polarized abelian varieties $A_g$ of genus g is defined over the integers and admits a minimal compactification $A_g^*$, also defined over the integers. The Hodge bundle over $A_g$ has its Chern classes in the Chow ring of $A_g$ with rational coefficients. We show that over the prime field $F_p$, these Chern classes naturally lift to $A_g^*$ and do so in the best possible way: despite the highly singular nature of $A_g^*$ they are represented by algebraic cycles on $A_g^*otimes F_p$ which define elements in its bivariant Chow ring. This is in contrast to the situation in the analytic topology, where these Chern classes have canonical lifts to the complex cohomology of the minimal compactification as Goresky-Pardon classes, which are known to define nontrivial Tate extensions inside the mixed Hodge structure on this cohomology.
{"title":"Lifting Chern classes by means of Ekedahl-Oort strata","authors":"G. Geer, E. Looijenga","doi":"10.2140/tunis.2021.3.469","DOIUrl":"https://doi.org/10.2140/tunis.2021.3.469","url":null,"abstract":"The moduli space of principally polarized abelian varieties $A_g$ of genus g is defined over the integers and admits a minimal compactification $A_g^*$, also defined over the integers. The Hodge bundle over $A_g$ has its Chern classes in the Chow ring of $A_g$ with rational coefficients. We show that over the prime field $F_p$, these Chern classes naturally lift to $A_g^*$ and do so in the best possible way: despite the highly singular nature of $A_g^*$ they are represented by algebraic cycles on $A_g^*otimes F_p$ which define elements in its bivariant Chow ring. This is in contrast to the situation in the analytic topology, where these Chern classes have canonical lifts to the complex cohomology of the minimal compactification as Goresky-Pardon classes, which are known to define nontrivial Tate extensions inside the mixed Hodge structure on this cohomology.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125152506","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 present a collection of research questions on cubic surfaces in 3-space. These questions inspired a collection of papers to be published in a special issue of the journal Le Matematiche. This article serves as the introduction to that issue. The number of questions is meant to match the number of lines on a cubic surface. We end with a list of problems that are open.
{"title":"Twenty-Seven Questions about the Cubic Surface.","authors":"K. Ranestad, B. Sturmfels","doi":"10.4418/2020.75.2.1","DOIUrl":"https://doi.org/10.4418/2020.75.2.1","url":null,"abstract":"We present a collection of research questions on cubic surfaces in 3-space. These questions inspired a collection of papers to be published in a special issue of the journal Le Matematiche. This article serves as the introduction to that issue. The number of questions is meant to match the number of lines on a cubic surface. We end with a list of problems that are open.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129391759","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}
Pub Date : 2019-12-16DOI: 10.1215/00192082-8720482
I. Biswas, Sorin Dumitrescu, C. Pauly
We define SL(r)-opers in the setup of vector bundles on curves with a parabolic structure over a divisor. Basic properties of these objects are investigated.
我们在除数上具有抛物结构的曲线上的向量束的建立中定义了SL(r)-算子。研究了这些物体的基本性质。
{"title":"Parabolic SL r -opers","authors":"I. Biswas, Sorin Dumitrescu, C. Pauly","doi":"10.1215/00192082-8720482","DOIUrl":"https://doi.org/10.1215/00192082-8720482","url":null,"abstract":"We define SL(r)-opers in the setup of vector bundles on curves with a parabolic structure over a divisor. Basic properties of these objects are investigated.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"121 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124171115","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}
Pub Date : 2019-12-15DOI: 10.17323/1609-4514-2021-21-3-453-466
M. Brion
Consider a normal projective variety $X$, a linear algebraic subgroup $G$ of Aut($X$), and the field $K$ of $G$-invariant rational functions on $X$. We show that the subgroup of Aut($X$) that fixes $K$ pointwise is linear algebraic. If $K$ has transcendence degree $1$ over $k$, then Aut($X$) is an algebraic group.
{"title":"Some Automorphism Groups are Linear Algebraic","authors":"M. Brion","doi":"10.17323/1609-4514-2021-21-3-453-466","DOIUrl":"https://doi.org/10.17323/1609-4514-2021-21-3-453-466","url":null,"abstract":"Consider a normal projective variety $X$, a linear algebraic subgroup $G$ of Aut($X$), and the field $K$ of $G$-invariant rational functions on $X$. We show that the subgroup of Aut($X$) that fixes $K$ pointwise is linear algebraic. If $K$ has transcendence degree $1$ over $k$, then Aut($X$) is an algebraic group.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125442801","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}
Pub Date : 2019-12-11DOI: 10.1142/s0129167x20501037
K. Hashizume
We study relations between two log minimal models of a fixed lc pair. For any two log minimal models of an lc pair constructed with log MMP, we prove that there are small birational models of the log minimal models which can be connected by a sequence of flops, and the two log minimal models share some properties. We also give examples of two log minimal models of an lc pair which have different properties.
{"title":"Relations between two log minimal models of log canonical pairs","authors":"K. Hashizume","doi":"10.1142/s0129167x20501037","DOIUrl":"https://doi.org/10.1142/s0129167x20501037","url":null,"abstract":"We study relations between two log minimal models of a fixed lc pair. For any two log minimal models of an lc pair constructed with log MMP, we prove that there are small birational models of the log minimal models which can be connected by a sequence of flops, and the two log minimal models share some properties. We also give examples of two log minimal models of an lc pair which have different properties.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"227 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122579717","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：