论文标题
重量功能，倾斜和稳定条件
Weight functions, tilts, and stability conditions
论文作者
论文摘要
在本文中，我们在一个框架中以国王，布里奇兰和拜耳的意义对待稳定条件。在国王之后，我们从三角剖分类别的权重功能开始，并考虑对三角形类别，T结构和稳定函数的越来越专业的配置，这些函数提供了稳定对象的等效类别。一路走来，我们在表示理论和代数几何形状中恢复现有结果，并在椭圆表面上证明了一系列新的结果，包括布里奇兰德稳定性条件和多项式稳定性条件的对应定理和多项式稳定性条件，局部有限性，用于Bridgeland稳定性条件的迷你壁的界限和界限。二维Bridgeland可半固定的物体，自动等效性在非零Kodaira尺寸的椭圆形表面上保留了几何布里奇兰的稳定性，以及Gepner方程的椭圆形表面的解决方案。
In this article, we treat stability conditions in the sense of King, Bridgeland and Bayer in a single framework. Following King, we begin with weight functions on a triangulated category, and consider increasingly specialised configurations of triangulated categories, t-structures and stability functions that give equivalent categories of stable objects. Along the way, we recover existing results in representation theory and algebraic geometry, and prove a series of new results on elliptic surfaces, including correspondence theorems for Bridgeland stability conditions and polynomial stability conditions, local finiteness and boundedness for mini-walls for Bridgeland stability conditions, isomorphisms between moduli of 1-dimensional twisted Gieseker semistable sheaves and 2-dimensional Bridgeland semistable objects, the preservation of geometric Bridgeland stability by autoequivalences on elliptic surfaces of nonzero Kodaira dimension, and solutions to Gepner equations on elliptic surfaces.
