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On a topological counterpart of regularization for holonomic 𝒟-modules 关于完整的正则化的拓扑对应物𝒟-modules
arXiv: Algebraic Geometry Pub Date : 2020-02-16 DOI: 10.5802/jep.140
A. D'agnolo, M. Kashiwara
{"title":"On a topological counterpart of regularization for holonomic 𝒟-modules","authors":"A. D'agnolo, M. Kashiwara","doi":"10.5802/jep.140","DOIUrl":"https://doi.org/10.5802/jep.140","url":null,"abstract":"On a complex manifold, the embedding of the category of regular holonomic D-modules into that of holonomic D-modules has a left quasi-inverse functor $mathcal{M}mapstomathcal{M}_{mathrm{reg}}$, called regularization. Recall that $mathcal{M}_{mathrm{reg}}$ is reconstructed from the de Rham complex of $mathcal{M}$ by the regular Riemann-Hilbert correspondence. Similarly, on a topological space, the embedding of sheaves into enhanced ind-sheaves has a left quasi-inverse functor, called here sheafification. Regularization and sheafification are intertwined by the irregular Riemann-Hilbert correspondence. Here, we study some of their properties. In particular, we provide a germ formula for the sheafification of enhanced specialization and microlocalization.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"131 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128302436","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: 6
Conic configurations via dual of quartic curves 四次曲线对偶的二次形
arXiv: Algebraic Geometry Pub Date : 2020-02-13 DOI: 10.1216/rmj.2021.51.721
X. Roulleau
{"title":"Conic configurations via dual of quartic curves","authors":"X. Roulleau","doi":"10.1216/rmj.2021.51.721","DOIUrl":"https://doi.org/10.1216/rmj.2021.51.721","url":null,"abstract":"We construct special conic configurations from some point configurations which are the singularities of the dual of a quartic curve.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127051812","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
38406501359372282063949 and All That: Monodromy of Fano Problems 38406501359372282063949和All That:单态法诺问题
arXiv: Algebraic Geometry Pub Date : 2020-02-11 DOI: 10.1093/imrn/rnaa275
Sachi Hashimoto, Borys Kadets
{"title":"38406501359372282063949 and All That: Monodromy of Fano Problems","authors":"Sachi Hashimoto, Borys Kadets","doi":"10.1093/imrn/rnaa275","DOIUrl":"https://doi.org/10.1093/imrn/rnaa275","url":null,"abstract":"A Fano problem is an enumerative problem of counting $r$-dimensional linear subspaces on a complete intersection in $mathbb{P}^n$ over a field of arbitrary characteristic, whenever the corresponding Fano scheme is finite. A classical example is enumerating lines on a cubic surface. We study the monodromy of finite Fano schemes $F_{r}(X)$ as the complete intersection $X$ varies. We prove that the monodromy group is either symmetric or alternating in most cases. In the exceptional cases, the monodromy group is one of the Weyl groups $W(E_6)$ or $W(D_k)$.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132046809","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: 7
Diagonal double Kodaira structures on finite groups. 有限群上的对角双Kodaira结构。
arXiv: Algebraic Geometry Pub Date : 2020-02-04 DOI: 10.1007/978-3-030-87502-2_12
F. Polizzi
{"title":"Diagonal double Kodaira structures on finite groups.","authors":"F. Polizzi","doi":"10.1007/978-3-030-87502-2_12","DOIUrl":"https://doi.org/10.1007/978-3-030-87502-2_12","url":null,"abstract":"","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124582691","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
On matrices of endomorphisms of abelian varieties 关于阿贝尔变体的自同态矩阵
arXiv: Algebraic Geometry Pub Date : 2020-02-01 DOI: 10.5802/mrr.5
Y. Zarhin
{"title":"On matrices of endomorphisms of abelian varieties","authors":"Y. Zarhin","doi":"10.5802/mrr.5","DOIUrl":"https://doi.org/10.5802/mrr.5","url":null,"abstract":"We study endomorphisms of abelian varieties and their action on the l-adic Tate modules. We prove that for every endomorphism one may choose a basis of each Tate module such that the corresponding matrix has rational entries and does not depend on l.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115357540","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
Linearly dependent and concise subsets of a Segre variety depending on k factors 一个分段的线性相关和简洁的子集取决于k个因素
arXiv: Algebraic Geometry Pub Date : 2020-02-01 DOI: 10.4134/BKMS.B200248
E. Ballico
{"title":"Linearly dependent and concise subsets of a Segre variety depending on k factors","authors":"E. Ballico","doi":"10.4134/BKMS.B200248","DOIUrl":"https://doi.org/10.4134/BKMS.B200248","url":null,"abstract":"We study linearly dependent subsets with prescribed cardinality, $s$, of a multiprojective space. If the set $S$ is a circuit, we give an upper bound on the number of factors of the minimal multiprojective space containing $S$, while if $S$ has higher dependency this may be not true without strong assumptions. We describe the dependent subsets $S$ with $#S=6$.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"164 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116594836","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
On moduli spaces of polarized Enriques surfaces 偏振Enriques曲面的模空间
arXiv: Algebraic Geometry Pub Date : 2020-01-29 DOI: 10.1016/j.matpur.2020.10.003
A. L. Knutsen
{"title":"On moduli spaces of polarized Enriques surfaces","authors":"A. L. Knutsen","doi":"10.1016/j.matpur.2020.10.003","DOIUrl":"https://doi.org/10.1016/j.matpur.2020.10.003","url":null,"abstract":"","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"151-152 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120628765","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: 10
The Exceptional Locus in the Bertini Irreducibility Theorem for a Morphism 一类态射Bertini不可约定理中的例外轨迹
arXiv: Algebraic Geometry Pub Date : 2020-01-23 DOI: 10.1093/imrn/rnaa182
B. Poonen, Kaloyan Slavov
{"title":"The Exceptional Locus in the Bertini Irreducibility Theorem for a Morphism","authors":"B. Poonen, Kaloyan Slavov","doi":"10.1093/imrn/rnaa182","DOIUrl":"https://doi.org/10.1093/imrn/rnaa182","url":null,"abstract":"We introduce a novel approach to Bertini irreducibility theorems over an arbitrary field, based on random hyperplane slicing over a finite field. Extending a result of Benoist, we prove that for a morphism $phi colon X to mathbb{P}^n$ such that $X$ is geometrically irreducible and the nonempty fibers of $phi$ all have the same dimension, the locus of hyperplanes $H$ such that $phi^{-1} H$ is not geometrically irreducible has dimension at most $operatorname{codim} phi(X)+1$. We give an application to monodromy groups above hyperplane sections.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"117 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124140335","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: 7
Non-polyhedral effective cones from the moduli space of curves 曲线模空间的非多面体有效锥
arXiv: Algebraic Geometry Pub Date : 2020-01-22 DOI: 10.1090/TRAN/8365
S. Mullane
{"title":"Non-polyhedral effective cones from the moduli space of curves","authors":"S. Mullane","doi":"10.1090/TRAN/8365","DOIUrl":"https://doi.org/10.1090/TRAN/8365","url":null,"abstract":"We show that the pseudoeffective cone of divisors $overline{text{Eff}}^1(overline{mathcal{M}}_{g,n})$ for $ggeq 2$ and $ngeq 2$ is not polyhedral by showing that the class of the fibre of the morphism forgetting one point forms an extremal round edge of the dual nef cone of curves $overline{text{Nef}}_1(overline{mathcal{M}}_{g,n})$.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128509630","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
Tschirnhaus transformations after Hilbert 希尔伯特之后的齐恩豪斯变换
arXiv: Algebraic Geometry Pub Date : 2020-01-17 DOI: 10.4171/LEM/66-3/4-9
J. Wolfson
{"title":"Tschirnhaus transformations after Hilbert","authors":"J. Wolfson","doi":"10.4171/LEM/66-3/4-9","DOIUrl":"https://doi.org/10.4171/LEM/66-3/4-9","url":null,"abstract":"Let RD(n) denote the minimum d for which there exists a formula for the roots of the general degree n polynomial using only algebraic functions of d or fewer variables. In 1927, Hilbert sketched how the 27 lines on a cubic surface could be used to construct a 4-variable formula for the general degree 9 polynomial (implying $RD(9)le 4$). In this paper, we turn Hilbert's sketch into a general method. We show this method produces best-to-date upper bounds on RD(n) for all n, improving earlier results of Hamilton, Sylvester, Segre and Brauer.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"1 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":"130889665","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: 8
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