Normal Crossings Singularities for Symplectic Topology:Structures

作     者：Mohammad FARAJZADEH-TEHRANI Mark MCLEAN Aleksey ZINGER Mohammad FARAJZADEH-TEHRANI;Mark MCLEAN;Aleksey ZINGER

作者机构：The University of IowaMacLean HallIowa CityIA 52241 Department of MathematicsStony Brook UniversityStony BrookNY 11794 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2024年第40卷第1期

页      面：107-160页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

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

主　　题：Normal crossings divisor Chern class Logarithmic tangent bundle 

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 *** 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 *** structures have applications in constructions and analysis of various moduli *** 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.