We give a brief overview of Bridgeland’s theory of stability conditions, focusing on applications to algebraic geometry. We sketch the basic ideas in Bayer’s proof of the Brill–Noether Theorem and in the authors’ proof of a theorem by Gruson–Peskine and Harris on the genus of space curves. This note originated from the lecture of the first author at the conference From Algebraic Geometry to Vision and AI: A Symposium Celebrating the Mathematical Work of David Mumford, held at the Center of Mathematical Sciences and Applications, Harvard University, August 18–20, 2018.

中文翻译：

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稳定性和应用

我们简要介绍了Bridgeland的稳定性条件理论，重点介绍了在代数几何中的应用。我们在拜耳的Brill-Noether定理证明和作者的Gruson-Peskine和Harris的关于空间曲线属的定理证明中，概述了基本思想。本笔记源于第一作者在从代数几何到视觉和人工智能的会议上的演讲：庆祝戴维·芒福德的数学工作研讨会，于2018年8月18日至20日在哈佛大学数学科学与应用中心举行。