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On the existence of harmonic $Z_2$ spinors 关于调和Z_2旋量的存在性
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2021-03-01 DOI: 10.4310/JDG/1615487003
Aleksander Doan, Thomas Walpuski
{"title":"On the existence of harmonic $Z_2$ spinors","authors":"Aleksander Doan, Thomas Walpuski","doi":"10.4310/JDG/1615487003","DOIUrl":"https://doi.org/10.4310/JDG/1615487003","url":null,"abstract":"We prove the existence of singular harmonic Z2 spinors on 3–manifolds with b1 > 1. The proof relies on a wall-crossing formula for solutions to the Seiberg–Witten equation with two spinors. The existence of singular harmonic Z2 spinors and the shape of our wall-crossing formula shed new light on recent observations made by Joyce [Joy17] regarding Donaldson and Segal’s proposal for counting G2–instantons [DS11].","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":"117 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42370502","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
Fukaya $A_infty$-structures associated to Lefschetz fibrations. III Fukaya $A_infty$ -与Lefschetz纤维相关的结构。3。
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2021-03-01 DOI: 10.4310/jdg/1615487005
Paul Seidel
{"title":"Fukaya $A_infty$-structures associated to Lefschetz fibrations. III","authors":"Paul Seidel","doi":"10.4310/jdg/1615487005","DOIUrl":"https://doi.org/10.4310/jdg/1615487005","url":null,"abstract":"Floer cohomology groups are usually defined over a field of formal functions (a Novikov field). Under certain assumptions, one can equip them with connections, which means operations of differentiation with respect to the Novikov variable. This allows one to write differential equations for Floer cohomology classes. Here, we apply that idea to symplectic cohomology groups associated to Lefschetz fibrations, and establish a relation with enumerative geometry.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":"19 4","pages":""},"PeriodicalIF":2.5,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503391","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: 0
From the Hitchin section to opers through nonabelian Hodge 从希钦部分到非贝利式霍奇的歌剧
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2021-02-01 DOI: 10.4310/JDG/1612975016
Olivia Dumitrescu, Laura Fredrickson, Georgios Kydonakis, R. Mazzeo, M. Mulase, A. Neitzke
{"title":"From the Hitchin section to opers through nonabelian Hodge","authors":"Olivia Dumitrescu, Laura Fredrickson, Georgios Kydonakis, R. Mazzeo, M. Mulase, A. Neitzke","doi":"10.4310/JDG/1612975016","DOIUrl":"https://doi.org/10.4310/JDG/1612975016","url":null,"abstract":"For a complex simple simply connected Lie group $G$, and a compact Riemann surface $C$, we consider two sorts of families of flat $G$-connections over $C$. Each family is determined by a point $mathbf{u}$ of the base of Hitchin’s integrable system for $(G,C)$. One family $nabla_{hbar ,mathbf{u}}$ consists of $G$-opers, and depends on $hbar in mathbb{C}^times$. The other family $nabla_{R, zeta,mathbf{u}}$ is built from solutions of Hitchin’s equations, and depends on $zeta in mathbb{C}^times , R in mathbb{R}^+$. We show that in the scaling limit $R to 0, zeta = hbar R$, we have $nabla_{R,zeta,mathbf{u}} to nabla_{hbar,mathbf{u}}$. This establishes and generalizes a conjecture formulated by Gaiotto.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":"117 1","pages":"223-253"},"PeriodicalIF":2.5,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45535930","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
Correspondence theorem between holomorphic discs and tropical discs on K3 surfaces K3表面上全纯盘与热带盘的对应定理
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2021-01-06 DOI: 10.4310/jdg/1609902017
Yu-Shen Lin
{"title":"Correspondence theorem between holomorphic discs and tropical discs on K3 surfaces","authors":"Yu-Shen Lin","doi":"10.4310/jdg/1609902017","DOIUrl":"https://doi.org/10.4310/jdg/1609902017","url":null,"abstract":"In this paper, we prove that the open Gromov–Witten invariants defined in [20] on K3 surfaces satisfy the Kontsevich–Soibelman wall-crossing formula. One hand, this gives a geometric interpretation of the slab functions in Gross–Siebert program. On the other hands, the open Gromov–Witten invariants coincide with the weighted counting of tropical discs. This is an analog of the corresponding theorem on toric varieties [26][27] but on compact Calabi–Yau surfaces.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":"20 4","pages":""},"PeriodicalIF":2.5,"publicationDate":"2021-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503390","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: 0
Limit of Weierstrass measure on stable curves 稳定曲线上Weierstrass测度的极限
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2020-12-17 DOI: 10.4310/jdg/1668186789
Ngai-fung Ng, Sai-Kee Yeung
{"title":"Limit of Weierstrass measure on stable curves","authors":"Ngai-fung Ng, Sai-Kee Yeung","doi":"10.4310/jdg/1668186789","DOIUrl":"https://doi.org/10.4310/jdg/1668186789","url":null,"abstract":"The goal of the paper is to study the limiting behavior of the Weierstrass measures on a smooth curve of genus $ggeqslant 2$ as the curve approaches a certain nodal stable curve represented by a point in the Deligne-Mumford compactification $overline{mathcal M}_g$ of the moduli $mathcal{M}_g$, including irreducible ones or those of compact type. As a consequence, the Weierstrass measures on a stable rational curve at the boundary of $mathcal{M}_g$ are completely determined. In the process, the asymptotic behavior of the Bergman measure is also studied.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":"1 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42515865","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: 0
Index to Volume 126 第126卷索引
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2020-12-03 DOI: 10.4310/jdg/1606964419
{"title":"Index to Volume 126","authors":"","doi":"10.4310/jdg/1606964419","DOIUrl":"https://doi.org/10.4310/jdg/1606964419","url":null,"abstract":"<p><strong>Source: </strong>Journal of Differential Geometry, Volume 116, Number 3</p>","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":"21 3","pages":""},"PeriodicalIF":2.5,"publicationDate":"2020-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503389","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: 0
New proof for the regularity of Monge–Ampère type equations 蒙日-安培尔型方程正则性的新证明
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2020-11-01 DOI: 10.4310/jdg/1606964417
Xu-jia Wang, Yating Wu
{"title":"New proof for the regularity of Monge–Ampère type equations","authors":"Xu-jia Wang, Yating Wu","doi":"10.4310/jdg/1606964417","DOIUrl":"https://doi.org/10.4310/jdg/1606964417","url":null,"abstract":"","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":"116 1","pages":"543-553"},"PeriodicalIF":2.5,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42466754","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
The $L_p$ Minkowski problem for the electrostatic $mathfrak{p}$-capacity 静电$mathfrak{p}$-容量的$L_p$ Minkowski问题
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2020-11-01 DOI: 10.4310/jdg/1606964418
Zou Du, Xiong Ge
{"title":"The $L_p$ Minkowski problem for the electrostatic $mathfrak{p}$-capacity","authors":"Zou Du, Xiong Ge","doi":"10.4310/jdg/1606964418","DOIUrl":"https://doi.org/10.4310/jdg/1606964418","url":null,"abstract":"","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":"116 1","pages":"555-596"},"PeriodicalIF":2.5,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46870650","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
Space of Ricci flows (II)—Part B: Weak compactness of the flows Ricci流的空间（II）——B部分：流的弱紧性
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2020-09-01 DOI: 10.4310/jdg/1599271253
Xiuxiong Chen, Bing Wang
{"title":"Space of Ricci flows (II)—Part B: Weak compactness of the flows","authors":"Xiuxiong Chen, Bing Wang","doi":"10.4310/jdg/1599271253","DOIUrl":"https://doi.org/10.4310/jdg/1599271253","url":null,"abstract":"","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":"116 1","pages":"1-123"},"PeriodicalIF":2.5,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48727375","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: 38
Riemann–Hilbert problems for the resolved conifold and non-perturbative partition functions 已解的共褶配分函数和非微扰配分函数的Riemann-Hilbert问题
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2020-07-01 DOI: 10.4310/jdg/1594260015
T. Bridgeland
{"title":"Riemann–Hilbert problems for the resolved conifold and non-perturbative partition functions","authors":"T. Bridgeland","doi":"10.4310/jdg/1594260015","DOIUrl":"https://doi.org/10.4310/jdg/1594260015","url":null,"abstract":"","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":"115 1","pages":"395-435"},"PeriodicalIF":2.5,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48491802","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
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