惯性聚合 高效追踪和阅读你感兴趣的博客、新闻、科技资讯
阅读原文 在惯性聚合中打开

推荐订阅源

博客园 - 三生石上(FineUI控件)
freeCodeCamp Programming Tutorials: Python, JavaScript, Git & More
月光博客
月光博客
博客园 - 【当耐特】
Hugging Face - Blog
Hugging Face - Blog
让小产品的独立变现更简单 - ezindie.com
让小产品的独立变现更简单 - ezindie.com
爱范儿
爱范儿
大猫的无限游戏
大猫的无限游戏
S
SegmentFault 最新的问题
博客园_首页
雷峰网
雷峰网
量子位
有赞技术团队
有赞技术团队
博客园 - 叶小钗
博客园 - 聂微东
V
V2EX
OSCHINA 社区最新新闻
OSCHINA 社区最新新闻
博客园 - 司徒正美
小众软件
小众软件
The Cloudflare Blog
阮一峰的网络日志
阮一峰的网络日志
Apple Machine Learning Research
Apple Machine Learning Research
Jina AI
Jina AI
人人都是产品经理
人人都是产品经理

math updates on arXiv.org

Coupling-Robust Accuracy in Multiphysics Physics Informed Neural Networks via Kronecker-Preconditioned Optimization Non-normal spectral signatures of instability in neural network training dynamics Optimization of randomized neural networks for transfer operator approximation Selective Ambulance Dispatch Under Contextual Travel-Time Uncertainty LLAMA LIMA: A Living Meta-Analysis on the Effects of Generative AI on Learning Mathematics Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations LLMs as Noisy Channels: A Shannon Perspective on Model Capacity and Scaling Laws On the Stability of Spherical Hellinger-Kantorovich Flows and Their Implications for Differential Privacy Training-Free Looped Transformers Move on Muon : A Hamiltonian probability gradient flow perspective of Muon optimizer Entrywise Error Bounds for Spectral Ranking with Semi-Random Adversaries Asymmetric Scaling Laws from Sparse Features Is Dimensionality a Barrier for Retrieval Models? RA-DCA: A Randomized Active-Set DCA for Directional Stationarity in Max-Structured DC Programs Commutator-Induced Uncertainty in VAEs Weisfeiler-Leman Is Incomplete on Simple Spectrum Graphs, so Canonicalize Them Sparse In-Network Learning via Shortest-Path Backpropagation and Finite-Rate Gating Instance-Optimal Estimation with Multiple LLM Judges on a Budget Entropy Equivalence Testing Expand More, Shrink Less: Shaping Effective-Rank Dynamics for Dense Scaling in Recommendation Any-Dimensional Invariant Universality Operationalizing Individual Fairness via Gradient Descent and Bradley-Terry Models Anytime Training with Schedule-Free Spectral Optimization Diffusion-based Denoising Beats Vanilla Score Matching in Parameter Estimation: A Theoretical Explanation Resilience Characterization of AI-Native Wireless Receivers via Persistent Homology The General Theory of Localization Methods Group-Algebraic Tensors: Provably-optimal Equivariant Learning and Physical Symmetry Discovery General Lower Bounds for Differentially Private Federated Learning with Arbitrary Public-Transcript Interactions PilotWiMAE: Pilot-Native Representation Learning for Wireless Channels Proximal basin hopping: global optimization with guarantees
Log canonical pairs with conjecturally minimal volume
[Submitted on 15 Aug 2023 (v1), last revised 22 May 2026 (this v · 2026-05-26 · via math updates on arXiv.org

View PDF HTML (experimental)

Abstract:We construct log canonical pairs $(X,B)$ with $B$ a nonzero reduced divisor and $K_X+B$ ample that have the smallest known volume. We conjecture that our examples have the smallest volume in each dimension. The conjecture is true in dimension 2, by Liu and Shokurov. The examples are weighted projective hypersurfaces that are not quasi-smooth.
We also develop an example for a related extremal problem. Esser constructed a klt Calabi-Yau variety which conjecturally has the smallest mld in each dimension (for example, mld $1/13$ in dimension 2 and $1/311$ in dimension 3). However, the example was only worked out completely in dimensions at most 18. We now prove the desired properties of Esser's example in all dimensions (in particular, determining its mld).

Submission history

From: Burt Totaro [view email]
[v1] Tue, 15 Aug 2023 20:50:29 UTC (23 KB)
[v2] Sat, 30 Dec 2023 01:50:53 UTC (23 KB)
[v3] Tue, 7 May 2024 00:21:36 UTC (24 KB)
[v4] Fri, 22 May 2026 18:22:28 UTC (24 KB)