Metric SYZ conjecture and non-archimedean geometry
英文摘要:
We show that assuming a conjecture in non-archimedean geometry, then a metric formulation of the SYZ conjecture can be proved in large generality.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
Yang Li
We show that assuming a conjecture in non-archimedean geometry, then a metric formulation of the SYZ conjecture can be proved in large generality.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
继续探索
We survey the metric aspects of the Strominger-Yau-Zaslow conjecture on the existence of special Lagrangian fibrations on Calabi-Yau manifolds near the large complex structure limit. We will discuss the diverse motivations for the conjectural picture, what the best hopes are, and a number of subtleties. The bulk of the survey highlights the role of pluripotential theory, and non-archimedean geometry in particular, with a list of open questions.
Hybrid toric varieties and the non-archimedean SYZ fibration on Calabi-Yau hypersurfaces
本文利用热带收缩构造了一类极大退化 Calabi-Yau 超曲面上的非阿基米德 SYZ 纤维化,并证明在离散对称性条件下其度量势沿纤维为常数。
Valuative independence and metric SYZ conjecture
本文在极化最大退化紧致Calabi-Yau流形存在canonical基和估值独立性条件下,证明了度量SYZ猜想。
We prove the metric version of the SYZ conjecture for a class of Calabi-Yau hypersurfaces inside toric Fano manifolds, by solving a variational problem whose minimizer may be interpreted as a global solution of the real Monge-Ampère equation on certain polytopes. This does not rely on discrete symmetry.
We produce special Lagrangian $T^n$-fibrations on the generic regions of some Calabi-Yau hypersurfaces in the Fermat family $X_s=\{ Z_0\ldots Z_{n+1}+ e^{-s} ( Z_0^{n+2}+ \ldots Z_{n+1}^{n+2} ) =0 \}\subset \mathbb{CP}^{n+1} $ near the large complex structure limit $s\to +\infty$.
We survey some recent developments in the direction of the Yau-Tian-Donaldson conjecture, which relates the existence of constant scalar curvature Kähler metrics to the algebro-geometric notion of K-stability. The emphasis is put on the use of pluripotential theory and the interpretation of K-stability in terms of non-Archimedean geometry.
Tropical and non-Archimedean Monge-Ampère equations for a class of Calabi-Yau hypersurfaces
本文研究了复射影空间中极大退化Calabi-Yau超曲面族的Berkovich空间及其骨架上的非阿基米德与tropical Monge-Ampère方程,证明了方程解的唯一性及导出关系,并结合Yang Li的工作支持了弱度量SYZ猜想。
The abundance and SYZ conjectures in families of hyperkahler manifolds
研究超凯勒流形上具有nef且非大第一陈类的全纯线丛的半丰性,通过引入Teichmuller空间并证明全局Torelli定理,建立半丰性的形变不变性。
SYZ and optimal transport stability of Weyl polytopes
本文证明了反身Weyl多胞体的最优传输稳定性,并据此推出弱度量SYZ猜想对相应环面Fano流形中的Dwork族以及中心对称光滑Fano环面流形成立。
Family Floer SYZ singularities for the conifold transition
该研究在族Floer语境下证明了锥面过渡SYZ猜想的数学精确版本,明确写出奇异T对偶纤维并证实其与镜像簇代数簇缺失点的对应关系,还提供了Berkovich几何中仿射环面纤维化的新例子。
The degeneration of Calabi-Yau 3-folds via 3-forms and the SYZ conjecture
该研究考察辛6维流形上不同轨道类型的3-形式,揭示Calabi-Yau结构退化所产生的不稳定3-形式的丰富几何性质,并为SYZ猜想提供新视角。
From complex to non-Archimedean geometry: an approach to the YTD conjecture
本文探讨了复数域上代数几何、解析几何和非阿基米德几何之间的关系,并提出了一个关于常标量曲率Kähler度量的Yau-Tian-Donaldson猜想的证明框架。
The SYZ Conjecture explains Mirror Symmetry between mirror Calabi-Yau 3-folds M,M' in terms of special Lagrangian fibrations f : M --> B and f' : M' --> B over the same base B, whose fibres are dual 3-tori, except for singular fibres. One of the main problems in proving the SYZ Conjecture (or even in finding the right statement of it) is that the singularities of special Lagrangian 3-folds and fibrations are poorly understood. This paper studies the singularities of special Lagrangian fibrations. Our main rigorous results are the construction of examples of special Lagrangian fibrations on ope…
Operations on transcendental non-Archimedean metrics
本文基于[DXZ23]的超越非阿基米德度量理论定义基本多次位势论运算,并证明Boucksom–Jonsson包络猜想的类比成立。
Family Floer SYZ conjecture for $A_n$ singularity
本文通过构建量子修正的T对称性,解决了一个关于A_n奇点的数学精确的SYZ猜想,展示了如何通过局部奇点模型的拼接来获得全球SYZ猜想的解决方案,如K3曲面,并提供了关于奇异纤维碰撞和辫群作用的明确证据。
Family Floer mirror space for local SYZ singularities
本文针对带 Gross Lagrangian 纤维化的环面 Calabi-Yau 流形,精确表述并证明含奇异纤维的 SYZ 镜像对应,揭示 Maurer-Cartan 集严格小于对偶奇异纤维。
This is a write-up of the author's talk in the conference "Algebraic Geometry in East Asia 2016" held at the University of Tokyo in January 2016. We give a survey on a series of papers of the author and his collaborators Daniel Pomerleano and Kazushi Ueda where we show how Strominger-Yau-Zaslow (SYZ) transforms can be applied to understand the geometry of Kontsevich's homological mirror symmetry (HMS) conjecture for certain local Calabi-Yau manifolds.
We derive a formula for non-Archimedean Monge-Ampère measures of big models. As applications, we derive a positive intersection formula for non-Archimedean Mabuchi functional, and further reduce the uniform Yau-Tian-Donaldson conjecture for polarized manifolds to a conjecture about the existence of approximate Zariski decompositions that satisfy some asymptotic vanishing condition.
We study the asymptotic behavior of volume forms on a degenerating family of compact complex manifolds. Under rather general conditions, we prove that the volume forms converge in a natural sense to a Lebesgue-type measure on a certain simplicial complex. In particular, this provides a measure-theoretic version of a conjecture by Kontsevich--Soibelman and Gross--Wilson, bearing on maximal degenerations of Calabi--Yau manifolds.
扫码添加微信好友,提出您的宝贵建议 👇
💡 备注请填写:网站反馈
发表机构由 AI 从论文文本抽取,如发现错误,欢迎反馈修正建议。