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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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
Virtual resolutions for a product of projective spaces 投影空间乘积的虚分辨率
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2017-03-22 DOI: 10.14231/ag-2020-013
Christine Berkesch Zamaere, D. Erman, Gregory G. Smith
{"title":"Virtual resolutions for a product of projective spaces","authors":"Christine Berkesch Zamaere, D. Erman, Gregory G. Smith","doi":"10.14231/ag-2020-013","DOIUrl":"https://doi.org/10.14231/ag-2020-013","url":null,"abstract":"Syzygies capture intricate geometric properties of a subvariety in projective space. However, when the ambient space is a product of projective spaces or a more general smooth projective toric variety, minimal free resolutions over the Cox ring are too long and contain many geometrically superfluous summands. In this paper, we construct some much shorter free complexes that better encode the geometry.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2017-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48695814","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: 39
The tropical superpotential for $mathbb{P}^2$ $mathbb｛P｝^2的热带超势$
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2017-03-22 DOI: 10.14231/ag-2020-002
T. Prince
{"title":"The tropical superpotential for $mathbb{P}^2$","authors":"T. Prince","doi":"10.14231/ag-2020-002","DOIUrl":"https://doi.org/10.14231/ag-2020-002","url":null,"abstract":"We present an extended worked example of the computation of the tropical superpotential considered by Carl--Pumperla--Siebert. In particular we consider an affine manifold associated to the complement of a non-singular genus one plane curve, and calculate the wall and chamber decomposition determined by the Gross--Siebert algorithm. Using the results of Carl--Pumperla--Siebert we determine the tropical superpotential, via broken line counts, in every chamber of this decomposition. The superpotential defines a Laurent polynomial in every chamber, which we demonstrate to be identical to the Laurent polynomials predicted by Coates--Corti--Galkin--Golyshev--Kaspzryk to be mirror to $mathbb{P}^2$.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2017-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43057538","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: 3
K�hlerness of moduli spaces of stable sheaves over non-projective K3 surfaces 非射影K3曲面上稳定轮轴模空间的K度
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2017-03-06 DOI: 10.14231/AG-2019-020
A. Perego
{"title":"K�hlerness of moduli spaces of stable sheaves over non-projective K3 surfaces","authors":"A. Perego","doi":"10.14231/AG-2019-020","DOIUrl":"https://doi.org/10.14231/AG-2019-020","url":null,"abstract":"We show that a moduli space of slope-stable sheaves over a K3 surface is an irreducible hyperk\"ahler manifold if and only if its second Betti number is the sum of its Hodge numbers $h^{2,0}$, $h^{1,1}$ and $h^{0,2}$.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2017-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49205594","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
The tautological ring of $mathcal{M}_{g,n}$ via Pandharipande�Pixton�Zvonkine $r$-spin relations 通过Pandharipande ` ` Pixton ` ` Zvonkine $r$-自旋关系的$mathcal{M}_{g,n}$的重言环
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2017-03-02 DOI: 10.14231/AG-2018-019
Reinier Kramer, Farrokh Labib, D. Lewanski, S. Shadrin
{"title":"The tautological ring of $mathcal{M}_{g,n}$ via Pandharipande�Pixton�Zvonkine $r$-spin relations","authors":"Reinier Kramer, Farrokh Labib, D. Lewanski, S. Shadrin","doi":"10.14231/AG-2018-019","DOIUrl":"https://doi.org/10.14231/AG-2018-019","url":null,"abstract":"We use relations in the tautological ring of the moduli spaces Mg,n derived by Pandharipande, Pixton, and Zvonkine from the Givental formula for the r-spin Witten class in order to obtain some restrictions on the dimensions of the tautological rings of the open moduli spacesMg,n. In particular, we give a new proof for the result of Looijenga (for n = 1) and Buryak et al. (for n > 2) that dimRg-1(Mg,n) ≤ n. We also give a new proof of the result of Looijenga (for n = 1) and Ionel (for arbitrary n > 1) that Ri(Mg,n) = 0 for i > g and give some estimates for the dimension of Ri(Mg,n) for i ≤ g - 2.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2017-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41775270","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
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