Polynomial Invariants and SAGBI Bases for Multi-screws

用于求解多项式系统的 SagbiHomotopy.jl 软件包

The SagbiHomotopy.jl package for solving polynomial systems

本文介绍 Julia 包 SagbiHomotopy.jl，通过基于 SAGBI 同伦选择最优起始系统，减少方形水平参数化多项式系统的路径跟踪数量。

SAGBI与Gröbner基检测

SAGBI and Gröbner Bases Detection

本文提出多项式环中SAGBI基的检测算法，发布Macaulay2和Julia的SagbiGbDetection软件包，并研究齐次SAGBI检测的计算复杂度。

Sagbi Bases of Cox-Nagata Rings

We degenerate Cox-Nagata rings to toric algebras by means of sagbi bases induced by configurations over the rational function field. For del Pezzo surfaces, this degeneration implies the Batyrev-Popov conjecture that these rings are presented by ideals of quadrics. For the blow-up of projective n-space at n+3 points, sagbi bases of Cox-Nagata rings establish a link between the Verlinde formula and phylogenetic algebraic geometry, and we use this to answer questions due to D'Cruz-Iarobbino and Buczynska-Wisniewski. Inspired by the zonotopal algebras of Holtz and Ron, our study emphasizes explic…

箭图半不变量与SAGBI基

Quiver semi-invariants and SAGBI bases

本文引入连环表这一推广半标准表的组合结构，证明其可索引箭图的Domokos-Zubkov半不变量，明确了广义克罗内克箭图对应SAGBI基的存在性及有限情形的显式构造。

SAGBI bases and Degeneration of Spherical Varieties to Toric Varieties

Let X \subset Proj(V) be a projective spherical G-variety, where V is a finite dimensional G-module and G = SP(2n, C). In this paper, we show that X can be deformed, by a flat deformation, to the toric variety corresponding to a convex polytope Δ(X). The polytope Δ(X) is the polytope fibred over the moment polytope of X with the Gelfand-Cetlin polytopes as fibres. We prove this by showing that if X is a horospherical variety, e.g. flag varieties and Grassmanians, the homogeneous coordinate ring of X can be embedded in a Laurent polynomial algebra and has a SAGBI basis with respect to a natural…

多项式子代数的计算复杂性

Computational Complexity of Polynomial Subalgebras

本文研究多项式子代数成员资格问题与次数界的计算复杂性，证明其EXPSPACE完全性及齐次情形的PSPACE完全性，并与理想情形及单项式代数进行比较。