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Properness criteria for families of coherent analytic spaces 相干解析空间族的性质准则
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2017-10-04 DOI: 10.14231/AG-2020-015
M. Toma
{"title":"Properness criteria for families of coherent analytic spaces","authors":"M. Toma","doi":"10.14231/AG-2020-015","DOIUrl":"https://doi.org/10.14231/AG-2020-015","url":null,"abstract":"We extend Langton's valuative criterion for families of coherent algebraic sheaves to a complex analytic set-up. As a consequence we derive a set of sufficient conditions for the compactness of a moduli space of semistable sheaves over a compact complex manifold. This applies also to some cases appearing in complex projective geometry not covered by previous results.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2017-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48270226","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: 4
Segre classes of tautological bundles on Hilbert schemes of surfaces Hilbert曲面方案上的重言丛的Segre类
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2017-08-21 DOI: 10.14231/AG-2019-010
C. Voisin
{"title":"Segre classes of tautological bundles on Hilbert schemes of surfaces","authors":"C. Voisin","doi":"10.14231/AG-2019-010","DOIUrl":"https://doi.org/10.14231/AG-2019-010","url":null,"abstract":"We first give an alternative proof, based on a simple geometric argument, of a result of Marian, Oprea and Pandharipande on top Segre classes of the tautological bundles on Hilbert schemes of $K3$ surfaces equipped with a line bundle. We then turn to the blow-up of $K3$ surface at one point and establish vanishing results for the corresponding top Segre classes in a certain range. This determines, at least theoretically, all top Segre classes of tautological bundles for any pair $(Sigma,H),,Hin {rm Pic},Sigma$.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2017-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43453053","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: 26
Derived category of moduli of pointed curves. I 点曲线模的导出范畴。我
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2017-08-21 DOI: 10.14231/AG-2020-026
Ana-Maria Castravet, J. Tevelev
{"title":"Derived category of moduli of pointed curves. I","authors":"Ana-Maria Castravet, J. Tevelev","doi":"10.14231/AG-2020-026","DOIUrl":"https://doi.org/10.14231/AG-2020-026","url":null,"abstract":"This is the first paper in the sequence devoted to derived category of moduli spaces of curves of genus $0$ with marked points. We develop several approaches to describe it equivariantly with respect to the action of the symmetric group permuting marked points. We construct an equivariant full exceptional collection on the Losev-Manin space which categorifies derangements.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2017-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43105964","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: 21
On the (non-)vanishing of syzygies of Segre embeddings 关于分段嵌入合子的(非)消失
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2017-08-12 DOI: 10.14231/AG-2019-026
Luke Oeding, Claudiu Raicu, Steven V. Sam
{"title":"On the (non-)vanishing of syzygies of Segre embeddings","authors":"Luke Oeding, Claudiu Raicu, Steven V. Sam","doi":"10.14231/AG-2019-026","DOIUrl":"https://doi.org/10.14231/AG-2019-026","url":null,"abstract":"We analyze the vanishing and non-vanishing behavior of the graded Betti numbers for Segre embeddings of products of projective spaces. We give lower bounds for when each of the rows of the Betti table becomes non-zero, and prove that our bounds are tight for Segre embeddings of products of P^1. This generalizes results of Rubei concerning the Green-Lazarsfeld property N_p for Segre embeddings. Our methods combine the Kempf-Weyman geometric technique for computing syzygies, the Ein-Erman-Lazarsfeld approach to proving non-vanishing of Betti numbers, and the theory of algebras with straightening laws.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2017-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44574229","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
Bounds on Wahl singularities from symplectic topology 辛拓扑中Wahl奇点的界
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2017-08-07 DOI: 10.14231/ag-2020-003
J. Evans, I. Smith
{"title":"Bounds on Wahl singularities from symplectic topology","authors":"J. Evans, I. Smith","doi":"10.14231/ag-2020-003","DOIUrl":"https://doi.org/10.14231/ag-2020-003","url":null,"abstract":"Let X be a minimal surface of general type with positive geometric genus ($b_+ > 1$) and let $K^2$ be the square of its canonical class. Building on work of Khodorovskiy and Rana, we prove that if X develops a Wahl singularity of length $ell$ in a Q-Gorenstein degeneration, then $ell leq 4K^2 + 7$. This improves on the current best-known upper bound due to Lee ($ell leq 400(K^2)^4$). Our bound follows from a stronger theorem constraining symplectic embeddings of certain rational homology balls in surfaces of general type. In particular, we show that if the rational homology ball $B_{p,1}$ embeds symplectically in a quintic surface, then $p leq 12$, partially answering the symplectic version of a question of Kronheimer.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2017-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45168633","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: 10
Euler-symmetric projective varieties 欧拉对称投影变体
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2017-07-21 DOI: 10.14231/ag-2020-011
Baohua Fu, Jun-Muk Hwang
{"title":"Euler-symmetric projective varieties","authors":"Baohua Fu, Jun-Muk Hwang","doi":"10.14231/ag-2020-011","DOIUrl":"https://doi.org/10.14231/ag-2020-011","url":null,"abstract":"Euler-symmetric projective varieties are nondegenerate projective varieties admitting many C*-actions of Euler type. They are quasi-homogeneous and uniquely determined by their fundamental forms at a general point. We show that Euler-symmetric projective varieties can be classified by symbol systems, a class of algebraic objects modeled on the systems of fundamental forms at general points of projective varieties. We study relations between the algebraic properties of symbol systems and the geometric properties of Euler-symmetric projective varieties. We describe also the relation between Euler-symmetric projective varieties of dimension n and equivariant compactifications of the vector group G_a^n.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2017-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45221600","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
On the rationality of Kawamata log terminal singularities in positive characteristic 关于Kawamata对数终端奇异性在正特征中的合理性
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2017-06-10 DOI: 10.14231/ag-2019-023
C. Hacon, J. Witaszek
{"title":"On the rationality of Kawamata log terminal singularities in positive characteristic","authors":"C. Hacon, J. Witaszek","doi":"10.14231/ag-2019-023","DOIUrl":"https://doi.org/10.14231/ag-2019-023","url":null,"abstract":"We show that there exists a natural number $p_0$ such that any three-dimensional Kawamata log terminal singularity defined over an algebraically closed field of characteristic $p>p_0$ is rational and in particular Cohen-Macaulay.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2017-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48455244","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: 37
Monodromy map for tropical Dolbeault cohomology 热带Dolbeault上同源的一元图
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2017-04-23 DOI: 10.14231/AG-2019-018
Yifeng Liu
{"title":"Monodromy map for tropical Dolbeault cohomology","authors":"Yifeng Liu","doi":"10.14231/AG-2019-018","DOIUrl":"https://doi.org/10.14231/AG-2019-018","url":null,"abstract":"We define monodromy maps for tropical Dolbeault cohomology of algebraic varieties over non-Archimedean fields. We propose a conjecture of Hodge isomorphisms via monodromy maps, and provide some evidence.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2017-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42782453","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
Classification of Enriques surfaces with finite automorphism group in characteristic 2 特征2上有限自同构群的Enriques曲面的分类
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2017-03-28 DOI: 10.14231/ag-2020-012
T. Katsura, S. Kondō, G. Martin
{"title":"Classification of Enriques surfaces with finite automorphism group in characteristic 2","authors":"T. Katsura, S. Kondō, G. Martin","doi":"10.14231/ag-2020-012","DOIUrl":"https://doi.org/10.14231/ag-2020-012","url":null,"abstract":"We classify supersingular and classical Enriques surfaces with finite automorphism group in characteristic 2 into 8 types according to their dual graphs of all $(-2)$-curves (nonsigular rational curves). We give examples of these Enriques surfaces together with their canonical coverings. It follows that the classification of all Enriques surfaces with finite automorphism group in any characteristics has been finished.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2017-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43226091","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: 14
Enriques surfaces with finite automorphism group in positive characteristic 具有正特征的有限自同构群的Enriques曲面
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2017-03-24 DOI: 10.14231/ag-2019-027
G. Martin
{"title":"Enriques surfaces with finite automorphism group in positive characteristic","authors":"G. Martin","doi":"10.14231/ag-2019-027","DOIUrl":"https://doi.org/10.14231/ag-2019-027","url":null,"abstract":"We classify Enriques surfaces with smooth K3 cover and finite automorphism group in arbitrary positive characteristic. The classification is the same as over the complex numbers except that some types are missing in small characteristics. Moreover, we give a complete description of the moduli of these surfaces. Finally, we realize all types of Enriques surfaces with finite automorphism group over the prime fields $mathbb{F}_p$ and $mathbb{Q}$ whenever they exist.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2017-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45200922","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: 24
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