弧空間上的積分理論及應用

Abstract

In this report, we discuss the topic of arc space and motivic inte-gration , including some important properties such as the formula of changing variable. With this formula we review Kontsevich’s theorem which states that the Hodge number of crepant resolution is indepen-dent of resolution. Besides, we also review Mustat¸ˇ a’s work that using the knowledge of arc space and motivic integration to give a differ-ent view toward log canonical threshold. At last, Batyrev’s work of proving McKay correspondence is discussed.