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Birational geometry of moduli spaces of sheaves and Bridgeland stability

机译:鞋面和桥梁稳定性的模型空间的自由派几何

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Moduli spaces of sheaves and Hilbert schemes of points have experienced a recent resurgence in interest in the past several years, due largely to new techniques arising from Bridgeland stability conditions and derived category methods. In particular, classical questions about the birational geometry of these spaces can be answered by using new tools such as the positivity lemma of Bayer and Macri. In this article we first survey classical results on moduli spaces of sheaves and their birational geometry. We then discuss the relationship between those classical results and the new techniques coming from Bridgeland stability, and discuss how cones of ample divisors on these spaces can be computed with these new methods. This survey expands upon the author's talk at the 2015 Bootcamp in Algcbraic Geometry preceding the 2015 AMS Summer Research Institute on Algebraic Geometry at the University of Utah.
机译:Moduli Space的船首和贝尔伯特积分方案在过去几年中经历了最近的兴趣中的重新疗效,这主要是由于勇敢的稳定条件和衍生类别方法产生的新技术。特别是,关于这些空间的自然几何形状的经典问题可以通过使用拜耳和宏的阳性引理等新工具来回答。在本文中,我们首先调查了滑轮的Moduli Spaces及其自由型几何形状的古典结果。然后,我们讨论了这些古典结果与来自Bridgeland稳定性的新技术的关系,并讨论了如何使用这些新方法计算在这些空间上的充足除数的锥体。本调查扩展了作者在2015年在犹他大学的AMS夏季几何论坛上的allcbraic几何中的2015年Bootcamp的谈话。

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