The characterization of (𝑛 − 1)-spheres with 𝑛 + 4 vertices having maximal Buchstaber number

Download

• Paper

Abstract

We present a computationally efficient algorithm that is suitable for graphic processing unit implementation. This algorithm enables the identification of all weak pseudo-manifolds that meet specific facet conditions, drawn from a given input set. We employ this approach to enumerate toric colorable seeds. Consequently, we achieve a comprehensive characterization of $(n-1)$-dimensional PL spheres with $n+4$ vertices that possess a maximal Buchstaber number. A primary focus of this research is the fundamental categorization of non-singular complete toric varieties of Picard number $4$. This classification serves as a valuable tool for addressing questions related to toric manifolds of Picard number $4$. Notably, we have determined which of these manifolds satisfy equality within an inequality regarding the number of minimal components in their rational curve space. This addresses a question posed by Chen, Fu, and Hwang in 2014 for this specific case.

Citation

Choi, Suyoung, Hyeontae Jang, and Mathieu Vallée. 2024. “The characterization of (𝑛 − 1)-spheres with 𝑛 + 4 vertices having maximal Buchstaber number.” Journal für die reine und angewandte Mathematik (Crelles Journal) 2024 (811): 267–292. https://doi.org/doi:10.1515/crelle-2024-0027

@article{Choi_Jang_Vallée_2024,
  author = {Suyoung Choi and Hyeontae Jang and Mathieu Vallée},
  year = {2024},
  title = {The characterization of (𝑛 − 1)-spheres with 𝑛 + 4 vertices having maximal Buchstaber number},
  journal = {J. Reine Angew. Math.},
  volume = {2024},
  number = {811},
  pages = {267–292},
  doi = {doi:10.1515/crelle-2024-0027},
}