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Generalized Donaldson–Thomas invariants via Kirwan blowups 通过柯万吹胀的广义唐纳森-托马斯不变式
IF 1.3 1区 数学
Journal of Differential Geometry Pub Date : 2024-07-01 DOI: 10.4310/jdg/1721071499
Jun Li, Y. Kiem, M. Savvas
{"title":"Generalized Donaldson–Thomas invariants via Kirwan blowups","authors":"Jun Li, Y. Kiem, M. Savvas","doi":"10.4310/jdg/1721071499","DOIUrl":"https://doi.org/10.4310/jdg/1721071499","url":null,"abstract":"Donaldson-Thomas (abbreviated as DT) theory is a sheaf theoretic technique of enumerating curves on a Calabi-Yau threefold. Classical DT invariants give a virtual count of Gieseker stable sheaves provided that no strictly semistable sheaves exist. This assumption was later lifted by the work of Joyce and Song who defined generalized DT invariants using Hall algebras and the Behrend function, their method being motivic in nature. In this talk, we will present a new approach towards generalized DT theory, obtaining an invariant as the degree of a virtual cycle inside a Deligne-Mumford stack. The main components are an adaptation of Kirwans partial desingularization procedure and recent results on the structure of moduli of sheaves on Calabi-Yau threefolds. Based on joint work with Young-Hoon Kiem and Jun Li. Special Note: Pre-talk at 1:30P. Host: James McKernan Friday, September 28, 2018 2:00 PM AP&M 5829 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141713159","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
Green's functions and complex Monge–Ampère equations 格林函数和复杂蒙日-安培方程
IF 1.3 1区 数学
Journal of Differential Geometry Pub Date : 2024-07-01 DOI: 10.4310/jdg/1721071497
Bin Guo, Duong H. Phong, Jacob Sturm
{"title":"Green's functions and complex Monge–Ampère equations","authors":"Bin Guo, Duong H. Phong, Jacob Sturm","doi":"10.4310/jdg/1721071497","DOIUrl":"https://doi.org/10.4310/jdg/1721071497","url":null,"abstract":"","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141705546","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: 1
Sharp existence, symmetry and asymptotics results for the singular $SU(3)$ Toda system with critical parameters 具有临界参数的奇异$SU(3)$ 托达系统的尖锐存在性、对称性和渐近性结果
IF 1.3 1区 数学
Journal of Differential Geometry Pub Date : 2024-07-01 DOI: 10.4310/jdg/1721071493
Zhijie Chen, Chang-Shou Lin
{"title":"Sharp existence, symmetry and asymptotics results for the singular $SU(3)$ Toda system with critical parameters","authors":"Zhijie Chen, Chang-Shou Lin","doi":"10.4310/jdg/1721071493","DOIUrl":"https://doi.org/10.4310/jdg/1721071493","url":null,"abstract":"","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141716251","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: 1
From Seiberg-Witten to Gromov: MCE and singular symplectic forms 从塞伯格-维滕到格罗莫夫：MCE 和奇异交映形式
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2024-06-01 DOI: 10.4310/jdg/1717772424
Yi-Jen Lee
{"title":"From Seiberg-Witten to Gromov: MCE and singular symplectic forms","authors":"Yi-Jen Lee","doi":"10.4310/jdg/1717772424","DOIUrl":"https://doi.org/10.4310/jdg/1717772424","url":null,"abstract":"","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141410231","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
Intersection de Rham complexes in positive characteristic 正特征相交德拉姆复合物
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2024-06-01 DOI: 10.4310/jdg/1717772421
Mao Sheng, Zebao Zhang
{"title":"Intersection de Rham complexes in positive characteristic","authors":"Mao Sheng, Zebao Zhang","doi":"10.4310/jdg/1717772421","DOIUrl":"https://doi.org/10.4310/jdg/1717772421","url":null,"abstract":"","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141395650","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
The dihedral rigidity conjecture for $n$-prisms n$ 棱镜的二面刚性猜想
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2024-01-01 DOI: 10.4310/jdg/1707767340
Chao Li
{"title":"The dihedral rigidity conjecture for $n$-prisms","authors":"Chao Li","doi":"10.4310/jdg/1707767340","DOIUrl":"https://doi.org/10.4310/jdg/1707767340","url":null,"abstract":"","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140525922","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
Local version of Courant’s nodal domain theorem 库朗结点域定理的局部版本
IF 2.5 1区 数学
Journal of Differential Geometry Pub Date : 2024-01-01 DOI: 10.4310/jdg/1707767334
Sagun Chanillo, A. Logunov, E. Malinnikova, D. Mangoubi
{"title":"Local version of Courant’s nodal domain theorem","authors":"Sagun Chanillo, A. Logunov, E. Malinnikova, D. Mangoubi","doi":"10.4310/jdg/1707767334","DOIUrl":"https://doi.org/10.4310/jdg/1707767334","url":null,"abstract":"","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140525585","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
Conical Calabi–Yau metrics on toric affine varieties and convex cones 环仿射变异和凸锥上的圆锥Calabi-Yau度量
1区 数学
Journal of Differential Geometry Pub Date : 2023-10-01 DOI: 10.4310/jdg/1696432924
Robert J. Berman
{"title":"Conical Calabi–Yau metrics on toric affine varieties and convex cones","authors":"Robert J. Berman","doi":"10.4310/jdg/1696432924","DOIUrl":"https://doi.org/10.4310/jdg/1696432924","url":null,"abstract":"It is shown that any affine toric variety $Y$, which is $mathbb{Q}$-Gorenstein, admits a conical Ricci flat Kähler metric, which is smooth on the regular locus of $Y$. The corresponding Reeb vector is the unique minimizer of the volume functional on the Reeb cone of $Y$. The case when the vertex point of $Y$ is an isolated singularity was previously shown by Futaki–Ono–Wang. The proof is based on an existence result for the inhomogeneous Monge–Ampère equation in $mathbb{R}^m$ with exponential right hand side and with prescribed target given by a proper convex cone, combined with transversal a priori estimates on $Y$.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135948526","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 index formula for families of Dirac type operators on pseudomanifolds 伪流形上狄拉克型算子族的指数公式
1区 数学
Journal of Differential Geometry Pub Date : 2023-10-01 DOI: 10.4310/jdg/1696432923
Pierre Albin, Jesse Gell-Redman
{"title":"The index formula for families of Dirac type operators on pseudomanifolds","authors":"Pierre Albin, Jesse Gell-Redman","doi":"10.4310/jdg/1696432923","DOIUrl":"https://doi.org/10.4310/jdg/1696432923","url":null,"abstract":"We study families of Dirac-type operators, with compatible perturbations, associated to wedge metrics on stratified spaces. We define a closed domain and, under an assumption of invertible boundary families, prove that the operators are self-adjoint and Fredholm with compact resolvents and trace-class heat kernels. We establish a formula for the Chern character of their index.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135948774","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
Existence of multiple closed CMC hypersurfaces with small mean curvature 具有小平均曲率的多个闭合CMC超曲面的存在性
1区 数学
Journal of Differential Geometry Pub Date : 2023-10-01 DOI: 10.4310/jdg/1696432925
Akashdeep Dey
{"title":"Existence of multiple closed CMC hypersurfaces with small mean curvature","authors":"Akashdeep Dey","doi":"10.4310/jdg/1696432925","DOIUrl":"https://doi.org/10.4310/jdg/1696432925","url":null,"abstract":"Min-max theory for constant mean curvature (CMC) hypersurfaces has been developed by Zhou–Zhu $[href{https://doi.org/10.1007/s00222-019-00886-1}{39}]$ and Zhou $[href{https://doi.org/10.4007/annals.2020.192.3.3}{38}]$. In particular, in $[href{https://doi.org/10.1007/s00222-019-00886-1}{39}]$, Zhou and Zhu proved that for any $c gt 0$, every closed Riemannian manifold $(M^{n+1}, g), 3 leq n + 1 leq 7$, contains a closed $c$-CMC hypersurface. In this article we will show that the min-max theory for CMC hypersurfaces in $[href{https://doi.org/10.1007/s00222-019-00886-1}{39}, href{https://doi.org/10.4007/annals.2020.192.3.3}{38}]$ can be extended in higher dimensions using the regularity theory of stable CMC hypersurfaces, developed by Bellettini–Wickramasekera $[href{https://doi.org/10.48550/arXiv.1802.00377}{4}, href{https://doi.org/10.48550/arXiv.1902.09669}{5}]$ and Bellettini–Chodosh–Wickramasekera $[href{https://doi.org/10.1016/j.aim.2019.05.023}{3}]$. Furthermore, we will prove that the number of closed $c$-CMC hypersurfaces in a closed Riemannian manifold $(M^{n+1}, g), n+1 geq 3$, tends to infinity as $c to 0^+$. More quantitatively, there exists a constant $gamma_0$, depending on $g$, such that for all $c gt 0$, there exist at least $gamma_0 c^{-frac{1}{n+1}}$ many closed $c$-CMC hypersurfaces (with optimal regularity) in $(M,g)$.","PeriodicalId":15642,"journal":{"name":"Journal of Differential Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135948783","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: 9
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