论文标题
类别的稳定性和正常的投射品种在完美领域
Stability in Categories and Normal Projective Varieties over Perfect Fields
论文作者
论文摘要
我们在任意类别中提出了$δ$稳定性和稳定性过滤的概念，这等同于对象上的硬纳拉西姆汉（HN）序列的存在。实际上，它等同于存在零形态的存在，对象上的部分顺序以及某些通用序列的集合。在嵌入在环境三角类别中的添加类别中，我们可以通过计算斜率序列和对象的欧拉特征来获得对象的数值多项式或中心电荷，从而诱导部分顺序和HN序列。在任意完美场上$ k $的正常投射表面的情况下，我们显示了$δ$属性在相关有限的派生类别上的存在，这等同于布里奇兰在正常表面上的稳定性。该结果还导致了对正常投影品种在完美领域的正常投射品种的新有效限制定理。我们的方法还提供了Hodge指数定理和Bogomolov不平等的替代证明。
We present a notion of $Δ$-stability and stability filtration in arbitrary categories which is equivalent to the existence of Harder-Narasimhan (HN) sequences on objects. Indeed it is equivalent to the existence of a zero morphism, a partial order on objects, and a collection of some universal sequences. In additive categories embedded in an ambient triangulated category, we could obtain a numerical polynomial or central charge of objects by calculating the Euler characteristic of slope sequences and objects, inducing a partial order and HN sequences. In the case of normal projective surfaces over an arbitrary perfect field $k$ we show the existence of $Δ$-stabilities of degree one on the relevant bounded derived categories which is equivalent to the existence of Bridgeland's stabilities on normal surfaces. This result also leads to new effective restriction theorem of slope semistable sheave on normal projective varieties over perfect fields. Our approach also gives alternative proofs of Hodge Index Theorem and Bogomolov Inequality.
