Normal Crossings Singularities for Symplectic Topology:Structures  

作　　者：Mohammad FARAJZADEH-TEHRANI Mark MCLEAN Aleksey ZINGER 

机构地区：[1]The University of Iowa,MacLean Hall,Iowa City,IA 52241 [2]Department of Mathematics,Stony Brook University,Stony Brook,NY 11794

出　　处：《Acta Mathematica Sinica,English Series》2024年第1期107-160,共54页数学学报（英文版）

基　　金：Supported by NSF grants DMS-2003340(F.Tehrani);DMS-1811861(Mclean);DMS-1901979(Zinger)。

摘　　要：Our previous papers introduce topological notions of normal crossings symplectic divisor and variety,show that they are equivalent,in a suitable sense,to the corresponding geometric notions,and establish a topological smoothability criterion for normal crossings symplectic varieties.The present paper constructs a blowup,a complex line bundle,and a logarithmic tangent bundle naturally associated with a normal crossings symplectic divisor and determines the Chern class of the last bundle.These structures have applications in constructions and analysis of various moduli spaces.As a corollary of the Chern class formula for the logarithmic tangent bundle,we refine Aluffi’s formula for the Chern class of the tangent bundle of the blowup at a complete intersection to account for the torsion and extend it to the blowup at the deepest stratum of an arbitrary normal crossings divisor.

关 键 词：Normal crossings divisor Chern class Logarithmic tangent bundle 

分 类 号：O189[理学—数学]