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Epijournal de Geometrie Algebrique最新文献

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IF 0.8
Epijournal de Geometrie Algebrique Pub Date : 2020-10-12 DOI: 10.3139/9783446467781.bm
M. Nitschke
{"title":"Index","authors":"M. Nitschke","doi":"10.3139/9783446467781.bm","DOIUrl":"https://doi.org/10.3139/9783446467781.bm","url":null,"abstract":"","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"7 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82695942","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
Einleitung
IF 0.8
Epijournal de Geometrie Algebrique Pub Date : 2020-10-12 DOI: 10.3139/9783446467781.001
M. Nitschke
{"title":"Einleitung","authors":"M. Nitschke","doi":"10.3139/9783446467781.001","DOIUrl":"https://doi.org/10.3139/9783446467781.001","url":null,"abstract":"","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"90 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80811515","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
Torus actions, Morse homology, and the Hilbert scheme of points on affine space 环面作用，莫尔斯同调，以及仿射空间上点的希尔伯特格式
IF 0.8
Epijournal de Geometrie Algebrique Pub Date : 2020-09-15 DOI: 10.46298/epiga.2021.6792
B. Totaro
{"title":"Torus actions, Morse homology, and the Hilbert scheme of points on\u0000 affine space","authors":"B. Totaro","doi":"10.46298/epiga.2021.6792","DOIUrl":"https://doi.org/10.46298/epiga.2021.6792","url":null,"abstract":"We formulate a conjecture on actions of the multiplicative group in motivic\u0000homotopy theory. In short, if the multiplicative group G_m acts on a\u0000quasi-projective scheme U such that U is attracted as t approaches 0 in G_m to\u0000a closed subset Y in U, then the inclusion from Y to U should be an\u0000A^1-homotopy equivalence.\u0000 We prove several partial results. In particular, over the complex numbers,\u0000the inclusion is a homotopy equivalence on complex points. The proofs use an\u0000analog of Morse theory for singular varieties. Application: the Hilbert scheme\u0000of points on affine n-space is homotopy equivalent to the subspace consisting\u0000of schemes supported at the origin.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70484196","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
Uniform K-stability of polarized spherical varieties 偏振球形品种的均匀k稳定性
IF 0.8
Epijournal de Geometrie Algebrique Pub Date : 2020-09-14 DOI: 10.46298/epiga.2022.9959
Thibaut Delcroix
{"title":"Uniform K-stability of polarized spherical varieties","authors":"Thibaut Delcroix","doi":"10.46298/epiga.2022.9959","DOIUrl":"https://doi.org/10.46298/epiga.2022.9959","url":null,"abstract":"We express notions of K-stability of polarized spherical varieties in terms\u0000of combinatorial data, vastly generalizing the case of toric varieties. We then\u0000provide a combinatorial sufficient condition of G-uniform K-stability by\u0000studying the corresponding convex geometric problem. Thanks to recent work of\u0000Chi Li and a remark by Yuji Odaka, this provides an explicitly checkable\u0000sufficient condition of existence of constant scalar curvature Kahler metrics.\u0000As a side effect, we show that, on several families of spherical varieties,\u0000G-uniform K-stability is equivalent to K-polystability with respect to\u0000G-equivariant test configurations for polarizations close to the anticanonical\u0000bundle.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"33 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70484714","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: 16
Algebraic subgroups of the plane Cremona group over a perfect field 完美域上平面Cremona群的代数子群
IF 0.8
Epijournal de Geometrie Algebrique Pub Date : 2020-08-09 DOI: 10.46298/epiga.2021.6715
Julia Schneider, Susanna Zimmermann
{"title":"Algebraic subgroups of the plane Cremona group over a perfect field","authors":"Julia Schneider, Susanna Zimmermann","doi":"10.46298/epiga.2021.6715","DOIUrl":"https://doi.org/10.46298/epiga.2021.6715","url":null,"abstract":"We show that any infinite algebraic subgroup of the plane Cremona group over\u0000a perfect field is contained in a maximal algebraic subgroup of the plane\u0000Cremona group. We classify the maximal groups, and their subgroups of rational\u0000points, up to conjugacy by a birational map.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48436961","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
Curve counting and S-duality 曲线计数和s对偶性
IF 0.8
Epijournal de Geometrie Algebrique Pub Date : 2020-07-06 DOI: 10.46298/epiga.2023.volume7.9818
S. Feyzbakhsh, Richard P. Thomas
{"title":"Curve counting and S-duality","authors":"S. Feyzbakhsh, Richard P. Thomas","doi":"10.46298/epiga.2023.volume7.9818","DOIUrl":"https://doi.org/10.46298/epiga.2023.volume7.9818","url":null,"abstract":"We work on a projective threefold $X$ which satisfies the Bogomolov-Gieseker\u0000conjecture of Bayer-Macr`i-Toda, such as $mathbb P^3$ or the quintic\u0000threefold.\u0000 We prove certain moduli spaces of 2-dimensional torsion sheaves on $X$ are\u0000smooth bundles over Hilbert schemes of ideal sheaves of curves and points in\u0000$X$.\u0000 When $X$ is Calabi-Yau this gives a simple wall crossing formula expressing\u0000curve counts (and so ultimately Gromov-Witten invariants) in terms of counts of\u0000D4-D2-D0 branes. These latter invariants are predicted to have modular\u0000properties which we discuss from the point of view of S-duality and\u0000Noether-Lefschetz theory.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70486029","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
Density of Arithmetic Representations of Function Fields 函数域算术表示的密度
IF 0.8
Epijournal de Geometrie Algebrique Pub Date : 2020-05-26 DOI: 10.46298/epiga.2022.6568
H. Esnault, M. Kerz
{"title":"Density of Arithmetic Representations of Function Fields","authors":"H. Esnault, M. Kerz","doi":"10.46298/epiga.2022.6568","DOIUrl":"https://doi.org/10.46298/epiga.2022.6568","url":null,"abstract":"We propose a conjecture on the density of arithmetic points in the\u0000deformation space of representations of the 'etale fundamental group in\u0000positive characteristic. This? conjecture has applications to 'etale\u0000cohomology theory, for example it implies a Hard Lefschetz conjecture. We prove\u0000the density conjecture in tame degree two for the curve $mathbb{P}^1setminus\u0000{0,1,infty}$. v2: very small typos corrected.v3: final. Publication in\u0000Epiga.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49454744","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
Complex reflection groups and K3 surfaces I 复反射群与K3曲面1
IF 0.8
Epijournal de Geometrie Algebrique Pub Date : 2020-05-09 DOI: 10.46298/epiga.2021.volume5.6573
C'edric Bonnaf'e, A. Sarti
{"title":"Complex reflection groups and K3 surfaces I","authors":"C'edric Bonnaf'e, A. Sarti","doi":"10.46298/epiga.2021.volume5.6573","DOIUrl":"https://doi.org/10.46298/epiga.2021.volume5.6573","url":null,"abstract":"We construct here many families of K3 surfaces that one can obtain as\u0000quotients of algebraic surfaces by some subgroups of the rank four complex\u0000reflection groups. We find in total 15 families with at worst\u0000$ADE$--singularities. In particular we classify all the K3 surfaces that can be\u0000obtained as quotients by the derived subgroup of the previous complex\u0000reflection groups. We prove our results by using the geometry of the weighted\u0000projective spaces where these surfaces are embedded and the theory of Springer\u0000and Lehrer-Springer on properties of complex reflection groups. This\u0000construction generalizes a previous construction by W. Barth and the second\u0000author.\u0000\u0000 Comment: 26 pages","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48952919","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
Exceptional collections on certain Hassett spaces 某些哈塞特空间的特殊收藏
IF 0.8
Epijournal de Geometrie Algebrique Pub Date : 2020-05-02 DOI: 10.46298/epiga.2021.volume4.6456
Ana-Maria Castravet, J. Tevelev
{"title":"Exceptional collections on certain Hassett spaces","authors":"Ana-Maria Castravet, J. Tevelev","doi":"10.46298/epiga.2021.volume4.6456","DOIUrl":"https://doi.org/10.46298/epiga.2021.volume4.6456","url":null,"abstract":"We construct an $S_2times S_n$ invariant full exceptional collection on\u0000Hassett spaces of weighted stable rational curves with $n+2$ markings and\u0000weights $(frac{1}{2}+eta, frac{1}{2}+eta,epsilon,ldots,epsilon)$, for\u0000$0<epsilon, etall1$ and can be identified with symmetric GIT quotients of\u0000$(mathbb{P}^1)^n$ by the diagonal action of $mathbb{G}_m$ when $n$ is odd,\u0000and their Kirwan desingularization when $n$ is even. The existence of such an\u0000exceptional collection is one of the needed ingredients in order to prove the\u0000existence of a full $S_n$-invariant exceptional collection on\u0000$overline{mathcal{M}}_{0,n}$. To prove exceptionality we use the method of\u0000windows in derived categories. To prove fullness we use previous work on the\u0000existence of invariant full exceptional collections on Losev-Manin spaces.\u0000\u0000 Comment: At the request of the referee, the paper arXiv:1708.06340 has been\u0000 split into two parts. This is the second of those papers (submitted). 36\u0000 pages","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70484521","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: 5
Group-theoretic Johnson classes and a non-hyperelliptic curve with torsion Ceresa class 群论Johnson类和具有扭转Ceresa类的非超椭圆曲线
IF 0.8
Epijournal de Geometrie Algebrique Pub Date : 2020-04-13 DOI: 10.46298/epiga.2023.volume7.6849
Dean Bisogno, Wanlin Li, Daniel Litt, P. Srinivasan
{"title":"Group-theoretic Johnson classes and a non-hyperelliptic curve with torsion Ceresa class","authors":"Dean Bisogno, Wanlin Li, Daniel Litt, P. Srinivasan","doi":"10.46298/epiga.2023.volume7.6849","DOIUrl":"https://doi.org/10.46298/epiga.2023.volume7.6849","url":null,"abstract":"Let l be a prime and G a pro-l group with torsion-free abelianization. We\u0000produce group-theoretic analogues of the Johnson/Morita cocycle for G -- in the\u0000case of surface groups, these cocycles appear to refine existing constructions\u0000when l=2. We apply this to the pro-l etale fundamental groups of smooth curves\u0000to obtain Galois-cohomological analogues, and discuss their relationship to\u0000work of Hain and Matsumoto in the case the curve is proper. We analyze many of\u0000the fundamental properties of these classes and use them to give an example of\u0000a non-hyperelliptic curve whose Ceresa class has torsion image under the l-adic\u0000Abel-Jacobi map.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70485276","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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