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Journal of Algebraic Geometry最新文献

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Moduli of formal torsors 形式环的模
IF 1.8 1区 数学
Journal of Algebraic Geometry Pub Date : 2017-09-06 DOI: 10.1090/jag/771
F. Tonini, Takehiko Yasuda
{"title":"Moduli of formal torsors","authors":"F. Tonini, Takehiko Yasuda","doi":"10.1090/jag/771","DOIUrl":"https://doi.org/10.1090/jag/771","url":null,"abstract":"We construct the moduli stack of torsors over the formal punctured disk in characteristic \u0000\u0000 \u0000 \u0000 p\u0000 >\u0000 0\u0000 \u0000 p>0\u0000 \u0000\u0000 for a finite group isomorphic to the semidirect product of a \u0000\u0000 \u0000 p\u0000 p\u0000 \u0000\u0000-group and a tame cyclic group. We prove that the stack is a limit of separated Deligne-Mumford stacks with finite and universally injective transition maps.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2017-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43555407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Categorical measures for finite group actions 有限群作用的范畴测度
IF 1.8 1区 数学
Journal of Algebraic Geometry Pub Date : 2017-09-02 DOI: 10.1090/JAG/768
Daniel Bergh, S. Gorchinskiy, M. Larsen, V. Lunts
{"title":"Categorical measures for finite group actions","authors":"Daniel Bergh, S. Gorchinskiy, M. Larsen, V. Lunts","doi":"10.1090/JAG/768","DOIUrl":"https://doi.org/10.1090/JAG/768","url":null,"abstract":"Given a variety with a finite group action, we compare its equivariant categorical measure, that is, the categorical measure of the corresponding quotient stack, and the categorical measure of the extended quotient. Using weak factorization for orbifolds, we show that for a wide range of cases that these two measures coincide. This implies, in particular, a conjecture of Galkin and Shinder on categorical and motivic zeta-functions of varieties. We provide examples showing that, in general, these two measures are not equal. We also give an example related to a conjecture of Polishchuk and Van den Bergh, showing that a certain condition in this conjecture is indeed necessary.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2017-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48691631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
Geometry of logarithmic forms and deformations of complex structures 几何的对数形式和复杂结构的变形
IF 1.8 1区 数学
Journal of Algebraic Geometry Pub Date : 2017-07-31 DOI: 10.1090/JAG/723
Kefeng Liu, S. Rao, Xueyuan Wan
{"title":"Geometry of logarithmic forms and deformations of complex structures","authors":"Kefeng Liu, S. Rao, Xueyuan Wan","doi":"10.1090/JAG/723","DOIUrl":"https://doi.org/10.1090/JAG/723","url":null,"abstract":"We present a new method to solve certain \u0000\u0000 \u0000 \u0000 \u0000 ∂\u0000 ¯\u0000 \u0000 \u0000 bar partial\u0000 \u0000\u0000-equations for logarithmic differential forms by using harmonic integral theory for currents on Kähler manifolds. The result can be considered as a \u0000\u0000 \u0000 \u0000 ∂\u0000 \u0000 \u0000 ∂\u0000 ¯\u0000 \u0000 \u0000 \u0000 partial bar partial\u0000 \u0000\u0000-lemma for logarithmic forms. As applications, we generalize the result of Deligne about closedness of logarithmic forms, give geometric and simpler proofs of Deligne’s degeneracy theorem for the logarithmic Hodge to de Rham spectral sequences at \u0000\u0000 \u0000 \u0000 E\u0000 1\u0000 \u0000 E_1\u0000 \u0000\u0000-level, as well as a certain injectivity theorem on compact Kähler manifolds.\u0000\u0000Furthermore, for a family of logarithmic deformations of complex structures on Kähler manifolds, we construct the extension for any logarithmic \u0000\u0000 \u0000 \u0000 (\u0000 n\u0000 ,\u0000 q\u0000 )\u0000 \u0000 (n,q)\u0000 \u0000\u0000-form on the central fiber and thus deduce the local stability of log Calabi-Yau structure by extending an iteration method to the logarithmic forms. Finally we prove the unobstructedness of the deformations of a log Calabi-Yau pair and a pair on a Calabi-Yau manifold by the differential geometric method.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2017-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/JAG/723","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60550963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 17
Parallel transport for vector bundles on 𝑝-adic varieties 𝑝-adic上矢量束的平行移动
IF 1.8 1区 数学
Journal of Algebraic Geometry Pub Date : 2017-07-17 DOI: 10.1090/jag/747
C. Deninger, A. Werner
{"title":"Parallel transport for vector bundles on 𝑝-adic varieties","authors":"C. Deninger, A. Werner","doi":"10.1090/jag/747","DOIUrl":"https://doi.org/10.1090/jag/747","url":null,"abstract":"We develop a theory of étale parallel transport for vector bundles with numerically flat reduction on a p p -adic variety. This construction is compatible with natural operations on vector bundles, Galois equivariant and functorial with respect to morphisms of varieties. In particular, it provides a continuous p p -adic representation of the étale fundamental group for every vector bundle with numerically flat reduction. The results in the present paper generalize previous work by the authors on curves. They can be seen as a p p -adic analog of higher-dimensional generalizations of the classical Narasimhan-Seshadri correspondence on complex varieties. Moreover, they provide new insights into Faltings’ p p -adic Simpson correspondence between small Higgs bundles and small generalized representations by establishing a class of vector bundles with vanishing Higgs field giving rise to actual (not only generalized) representations.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2017-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/jag/747","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49655222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 13
A decomposition theorem for projective manifolds with nef anticanonical bundle 具有网络反正则束的射影流形的分解定理
IF 1.8 1区 数学
Journal of Algebraic Geometry Pub Date : 2017-06-27 DOI: 10.1090/JAG/715
Junyan Cao, A. Horing
{"title":"A decomposition theorem for projective manifolds with nef anticanonical bundle","authors":"Junyan Cao, A. Horing","doi":"10.1090/JAG/715","DOIUrl":"https://doi.org/10.1090/JAG/715","url":null,"abstract":"Let \u0000\u0000 \u0000 X\u0000 X\u0000 \u0000\u0000 be a simply connected projective manifold with nef anticanonical bundle. We prove that \u0000\u0000 \u0000 X\u0000 X\u0000 \u0000\u0000 is a product of a rationally connected manifold and a manifold with trivial canonical bundle. As an application we describe the MRC-fibration of any projective manifold with nef anticanonical bundle.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2017-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/JAG/715","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44568805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 50
Boundedness questions for Calabi–Yau threefolds Calabi-Yau的三倍有界性问题
IF 1.8 1区 数学
Journal of Algebraic Geometry Pub Date : 2017-06-05 DOI: 10.1090/JAG/781
P. Wilson
{"title":"Boundedness questions for Calabi–Yau threefolds","authors":"P. Wilson","doi":"10.1090/JAG/781","DOIUrl":"https://doi.org/10.1090/JAG/781","url":null,"abstract":"In this paper, we study boundedness questions for (simply connected) smooth Calabi–Yau threefolds. The diffeomorphism class of such a threefold is known to be determined up to finitely many possibilities by the integral middle cohomology and two integral forms on the integral second cohomology, namely the cubic cup-product form and the linear form given by cup-product with the second Chern class. The motivating question for this paper is whether knowledge of these cubic and linear forms determines the threefold up to finitely many families, that is the moduli of such threefolds is bounded. If this is true, then in particular the middle integral cohomology would be bounded by knowledge of these two forms.\u0000\u0000Crucial to this question is the study of rigid non-movable surfaces on the threefold, which are the irreducible surfaces that deform with any small deformation of the complex structure of the threefold but for which no multiple moves on the threefold. If for instance there are no such surfaces, then the answer to the motivating question is yes (Theorem 0.1). In particular, for given cubic and linear forms on the second cohomology, there must exist such surfaces for large enough third Betti number (Corollary 0.2).\u0000\u0000The paper starts by proving general results on these rigid non-movable surfaces and boundedness of the family of threefolds. The basic principle is that if the cohomology classes of these surfaces are also known, then boundedness should hold (Theorem 4.5). The second half of the paper restricts to the case of Picard number 2, where it is shown that knowledge of the cubic and linear forms does indeed bound the family of Calabi–Yau threefolds (Theorem 0.3). This appears to be the first non-trivial case where a general boundedness result for Calabi–Yau threefolds has been proved (without the assumption of a special structure).","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2017-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44857653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 13
PD Higgs crystals and Higgs cohomology in characteristic PD希格斯晶体与希格斯上同调特性
IF 1.8 1区 数学
Journal of Algebraic Geometry Pub Date : 2017-05-26 DOI: 10.1090/JAG/699
Hideto Oyama
{"title":"PD Higgs crystals and Higgs cohomology in characteristic","authors":"Hideto Oyama","doi":"10.1090/JAG/699","DOIUrl":"https://doi.org/10.1090/JAG/699","url":null,"abstract":"","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2017-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/JAG/699","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47044659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
Cones of Heegner divisors Heegner除数的Cones
IF 1.8 1区 数学
Journal of Algebraic Geometry Pub Date : 2017-05-16 DOI: 10.1090/JAG/734
J. Bruinier, M. Moller
{"title":"Cones of Heegner divisors","authors":"J. Bruinier, M. Moller","doi":"10.1090/JAG/734","DOIUrl":"https://doi.org/10.1090/JAG/734","url":null,"abstract":"We show that the cone of primitive Heegner divisors is finitely generated for many orthogonal Shimura varieties, including the moduli space of polarized \u0000\u0000 \u0000 \u0000 K\u0000 3\u0000 \u0000 K3\u0000 \u0000\u0000-surfaces. The proof relies on the growth of coefficients of modular forms.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2017-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/JAG/734","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48079677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
On rigid varieties with projective reduction 关于具有投影约简的刚性变种
IF 1.8 1区 数学
Journal of Algebraic Geometry Pub Date : 2017-04-11 DOI: 10.1090/jag/740
Shizhang Li
{"title":"On rigid varieties with projective reduction","authors":"Shizhang Li","doi":"10.1090/jag/740","DOIUrl":"https://doi.org/10.1090/jag/740","url":null,"abstract":"In this paper, we study smooth proper rigid varieties which admit formal models whose special fibers are projective. The Main Theorem asserts that the identity components of the associated rigid Picard varieties will automatically be proper. Consequently, we prove that \u0000\u0000 \u0000 p\u0000 p\u0000 \u0000\u0000-adic Hopf varieties will never have a projective reduction. The proof of our Main Theorem uses the theory of moduli of semistable coherent sheaves.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2017-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/jag/740","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49053961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
Stability of associated forms 关联形式的稳定性
IF 1.8 1区 数学
Journal of Algebraic Geometry Pub Date : 2017-03-01 DOI: 10.1090/JAG/719
M. Fedorchuk, A. Isaev
{"title":"Stability of associated forms","authors":"M. Fedorchuk, A. Isaev","doi":"10.1090/JAG/719","DOIUrl":"https://doi.org/10.1090/JAG/719","url":null,"abstract":"We show that the associated form, or, equivalently, a Macaulay inverse system, of an Artinian complete intersection of type \u0000\u0000 \u0000 \u0000 (\u0000 d\u0000 ,\u0000 …\u0000 ,\u0000 d\u0000 )\u0000 \u0000 (d,dots , d)\u0000 \u0000\u0000 is polystable. As an application, we obtain an invariant-theoretic variant of the Mather-Yau theorem for homogeneous hypersurface singularities.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2017-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/JAG/719","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49202850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
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