Скачать или смотреть Nathan Grieve : On Harder-Narasimhan data and the Central Limit Theorem

Starting with the work of Harder and Narasimhan, the concept of canonical (Harder and Narasimhan) filtration emerged as a fundamental tool for measuring the extent to which a given object in a suitable category fails to be slope semistable. In this lecture, I will discuss an abstract concept of Harder and Narasimhan data which I formulated as a tool for expanding on the key technical techniques of Codogni and Patakfalvi, which arise in their work on weak positivity of the CM line bundle over the moduli stack of K-semistable Fano varieties. Another source of motivation is Grayson's lattice reduction theory via slope semistability. Finally, via theory of Faltings and Wustholz, for slope semistabilty of filtered vector spaces, there is a strong overlap with techniques from Diophantine approximation for linear series. As application of this circle of ideas, I will explain a recent result which gives a filtered vector space analogue to the above mentioned key technical result of Codogni and Patakfalvi.