陳榮凱臺灣大學：數學研究所周致圻Chou, Chih-ChiChih-ChiChou2007-11-282018-06-282007-11-282018-06-282006http://ntur.lib.ntu.edu.tw//handle/246246/59473In 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.1 Introduction 3 2 Arc Space and Motivic Intergration 3 2.1 Some Lemmas . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Arc Space and Motivic Measure . . . . . . . . . . . . . . . . . 5 2.3 Motivic Integration . . . . . . . . . . . . . . . . . . . . . . . . 10 3 Log Canonical Threshold 17 3.1 Introduction to the Main Theorem . . . . . . . . . . . . . . . 17 3.2 Some Geometry Properties of Arc Space . . . . . . . . . . . . 20 3.3 Proof of Theorem 3.1 . . . . . . . . . . . . . . . . . . . . . . . 22 4 McKay Correspondence 23 4.1 Special Case for Toric Variety . . . . . . . . . . . . . . . . . . 24 4.2 Some Lemmas and Definitions . . . . . . . . . . . . . . . . . . 29 4.2.1 Log Pair (X, X) . . . . . . . . . . . . . . . . . . . . . 29 4.2.2 Orbifold E − function . . . . . . . . . . . . . . . . . . 30 4.3 Batyrev’s proof of McKay correspondece . . . . . . . . . . . . 35 5 References 38327233 bytesapplication/pdfen-US弧空間motivic integrationthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/59473/1/ntu-95-R93221033-1.pdf