{"title":"CARTAN GEOMETRIES ON COMPLEX MANIFOLDS OF ALGEBRAIC DIMENSION ZERO","authors":"I. Biswas, Sorin Dumitrescu, B. McKay","doi":"10.46298/epiga.2019.volume3.4460","DOIUrl":"https://doi.org/10.46298/epiga.2019.volume3.4460","url":null,"abstract":"International audience\u0000 \u0000 We show that compact complex manifolds of algebraic dimension zero bearing a holomorphic Cartan geometry of algebraic type have infinite fundamental group. This generalizes the main Theorem in [DM] where the same result was proved for the special cases of holomorphic affine connections and holomorphic conformal structures.\u0000 \u0000 \u0000 Nous montrons que toute variété complexe compacte de dimension algébrique nulle possédant une géométrie de Cartan holomorphe de type algébrique doit avoir un groupe fondamental infini. Il s’agit d’une généralisation du théorème principal de [DM] où le même résultat était montré dans le cas particulier des connexions affines holomorphes et des structures conformes holomorphes.\u0000","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70482685","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}
{"title":"The spectral gluing theorem revisited","authors":"Dario Beraldo","doi":"10.46298/epiga.2020.volume4.5940","DOIUrl":"https://doi.org/10.46298/epiga.2020.volume4.5940","url":null,"abstract":"We strengthen the gluing theorem occurring on the spectral side of the\u0000geometric Langlands conjecture. While the latter embeds $IndCoh_N(LS_G)$ into a\u0000category glued out of 'Fourier coefficients' parametrized by standard\u0000parabolics, our refinement explicitly identifies the essential image of such\u0000embedding.\u0000","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47726850","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}
{"title":"Explicit equations of the Cartwright-Steger surface","authors":"L. Borisov, Sai-Kee Yeung","doi":"10.46298/epiga.2020.volume4.5662","DOIUrl":"https://doi.org/10.46298/epiga.2020.volume4.5662","url":null,"abstract":"We construct explicit equations of Cartwright-Steger and related surfaces.\u0000\u0000 Comment: 16 pages, LaTeX","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48502364","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}
{"title":"Smooth affine group schemes over the dual numbers","authors":"M. Romagny, D. Tossici","doi":"10.46298/epiga.2019.volume3.4792","DOIUrl":"https://doi.org/10.46298/epiga.2019.volume3.4792","url":null,"abstract":"International audience\u0000 We provide an equivalence between the category of affine, smooth group schemes over the ring of generalized dual numbers $k[I]$, and the category of extensions of the form $1 to text{Lie}(G, I) to E to G to 1$ where G is an affine, smooth group scheme over k. Here k is an arbitrary commutative ring and $k[I] = k oplus I$ with $I^2 = 0$. The equivalence is given by Weil restriction, and we provide a quasi-inverse which we call Weil extension. It is compatible with the exact structures and the $mathbb{O}_k$-module stack structures on both categories. Our constructions rely on the use of the group algebra scheme of an affine group scheme; we introduce this object and establish its main properties. As an application, we establish a Dieudonné classification for smooth, commutative, unipotent group schemes over $k[I]$.\u0000 Nous construisons une équivalence entre la catégorie des schémas en groupes affines et lisses sur l'anneau des nombres duaux généralisés k[I], et la catégorie des extensions de la forme 1 → Lie(G, I) → E → G → 1 où G est un schéma en groupes affine, lisse sur k. Ici k est un anneau commutatif arbitraire et k[I] = k ⊕ I avec I 2 = 0. L'équivalence est donnée par la restriction de Weil, et nous construisons un foncteur quasi-inverse explicite que nous appelons extension de Weil. Ces foncteurs sont compatibles avec les structures exactes et avec les structures de champs en O k-modules des deux catégories. Nos constructions s'appuient sur le schéma en algèbres de groupe d'un schéma en groupes affines, que nous introduisons et dont nous donnons les propriétés principales. En application, nous donnons une classification de Dieudonné pour les schémas en groupes commutatifs, lisses, unipotents sur k[I] lorsque k est un corps parfait.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70483239","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}
{"title":"Sur l'hyperbolicit'e de graphes associ'es au groupe de Cremona","authors":"Anne Lonjou","doi":"10.46298/epiga.2019.volume3.4895","DOIUrl":"https://doi.org/10.46298/epiga.2019.volume3.4895","url":null,"abstract":"To reinforce the analogy between the mapping class group and the Cremona\u0000group of rank $2$ over an algebraic closed field, we look for a graph\u0000analoguous to the curve graph and such that the Cremona group acts on it\u0000non-trivially. A candidate is a graph introduced by D. Wright. However, we\u0000demonstrate that it is not Gromov-hyperbolic. This answers a question of A.\u0000Minasyan and D. Osin. Then, we construct two graphs associated to a Vorono\"i\u0000tesselation of the Cremona group introduced in a previous work of the autor. We\u0000show that one is quasi-isometric to the Wright graph. We prove that the second\u0000one is Gromov-hyperbolic.\u0000\u0000 Comment: 29 pages, en Franc{c}ais","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2018-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70483421","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}
{"title":"Limits of the trivial bundle on a curve","authors":"A. Beauville","doi":"10.46298/epiga.2018.volume2.4454","DOIUrl":"https://doi.org/10.46298/epiga.2018.volume2.4454","url":null,"abstract":"We attempt to describe the rank 2 vector bundles on a curve C which are\u0000specializations of the trivial bundle. We get a complete classifications when C\u0000is Brill-Noether generic, or when it is hyperelliptic; in both cases all limit\u0000vector bundles are decomposable. We give examples of indecomposable limit\u0000bundles for some special curves.\u0000\u0000 Comment: Final version, published in Epiga","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2017-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70483102","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}
{"title":"On the group of zero-cycles of holomorphic symplectic varieties","authors":"A. Marian, Xiaolei Zhao","doi":"10.46298/epiga.2020.volume4.5506","DOIUrl":"https://doi.org/10.46298/epiga.2020.volume4.5506","url":null,"abstract":"For a moduli space of Bridgeland-stable objects on a K3 surface, we show that\u0000the Chow class of a point is determined by the Chern class of the corresponding\u0000object on the surface. This establishes a conjecture of Junliang Shen, Qizheng\u0000Yin, and the second author.\u0000","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2017-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47642085","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}
{"title":"Prime Fano threefolds of genus 12 with a $G_m$-action","authors":"A. Kuznetsov, Yuri Prokhorov","doi":"10.46298/epiga.2018.volume2.4179","DOIUrl":"https://doi.org/10.46298/epiga.2018.volume2.4179","url":null,"abstract":"We give an explicit construction of prime Fano threefolds of genus 12 with a\u0000$G_m$-action, describe their isomorphism classes and automorphism groups.\u0000\u0000 Comment: 14 pages, LaTeX, updated version, to appear in 'Epijournal de\u0000 G'eom'etrie Alg'ebrique, Vol. 2 (2018), Article Nr. 3","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2017-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70482506","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}
{"title":"Lefschetz (1,1)-theorem in tropical geometry","authors":"Philipp Jell, Johannes Rau, Kristin M. Shaw","doi":"10.46298/epiga.2018.volume2.4126","DOIUrl":"https://doi.org/10.46298/epiga.2018.volume2.4126","url":null,"abstract":"For a tropical manifold of dimension n we show that the tropical homology\u0000classes of degree (n-1, n-1) which arise as fundamental classes of tropical\u0000cycles are precisely those in the kernel of the eigenwave map. To prove this we\u0000establish a tropical version of the Lefschetz (1, 1)-theorem for rational\u0000polyhedral spaces that relates tropical line bundles to the kernel of the wave\u0000homomorphism on cohomology. Our result for tropical manifolds then follows by\u0000combining this with Poincar'e duality for integral tropical homology.\u0000\u0000 Comment: 27 pages, 6 figures, published version","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2017-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70482420","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}
{"title":"A characterization of finite vector bundles on Gauduchon astheno-Kahler\u0000 manifolds","authors":"I. Biswas, Vamsi Pingali","doi":"10.46298/epiga.2018.volume2.4209","DOIUrl":"https://doi.org/10.46298/epiga.2018.volume2.4209","url":null,"abstract":"A vector bundle E on a projective variety X is called finite if it satisfies\u0000a nontrivial polynomial equation with integral coefficients. A theorem of Nori\u0000implies that E is finite if and only if the pullback of E to some finite etale\u0000Galois covering of X is trivial. We prove the same statement when X is a\u0000compact complex manifold admitting a Gauduchon astheno-Kahler metric.\u0000","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2017-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70483021","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}
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