MOTIVIC VIRTUAL SIGNED EULER CHARACTERISTICS AND THEIR APPLICATIONS TO VAFA-WITTEN INVARIANTS  

作　　者：Yunfeng JIANG 

机构地区：[1]College of Mathematics and Statistics,Shenzhen University,Shenzhen 518060,China Department of Mathematics,University of Kansas,KS 66045,USA

出　　处：《Acta Mathematica Scientia》2022年第6期2279-2300,共22页数学物理学报（B辑英文版）

摘　　要：For any scheme M with a perfect obstruction theory,Jiang and Thomas associated a scheme N with a symmetric perfect obstruction theory.The scheme N is a cone over M given by the dual of the obstruction sheaf of M,and contains M as its zero section.Locally,N is the critical locus of a regular function.In this note we prove that N is a d-critical scheme in the sense of Joyce.There exists a global motive for N locally given by the motive of the vanishing cycle of the local regular function.We prove a motivic localization formula under the good and circle compact C*-action for N.When taking the Euler characteristic,the weighted Euler characteristic of N weighted by the Behrend function is the signed Euler characteristic of M by motivic method.As applications,using the main theorem we study the motivic generating series of the motivic Vafa-Witten invariants for K3 surfaces.

关 键 词：motivic Euler characteristics dual obstruction cone motivic Vafa-Witten invariants K3 surfaces 

分 类 号：O186.1[理学—数学]