The Homology Growth for Finite Abelian Covers of Smooth Quasi-projective Varieties  

作　　者：Fenglin LI Yongqiang LIU 

机构地区：[1]School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China [2]Institute of Geometry and Physics,University of Science and Technology of China,Hefei 230026,China

出　　处：《Chinese Annals of Mathematics,Series B》2025年第1期51-62,共12页数学年刊(B辑英文版)

基　　金：supported by the National Key Research and Development Project(No.SQ2020YFA070080);the National Natural Science Foundation of China(No.12001511);the Project of Stable Support for Youth Team in Basic Research Field CAS(No.YSBR-001);the Project of Analysis and Geometry on Bundles of the Ministry of Science and Technology of China and the Fundamental Research Funds for the Central Universities。

摘　　要：Let X be a complex smooth quasi-projective variety with a fixed epimorphism ν:π_(1)(X)■H,where H is a finitely generated abelian group with rank H≥1.In this paper,the authors study the asymptotic behaviour of Betti numbers with all possible field coefficients and the order of the torsion subgroup of singular homology associated toν,known as the L^(2)-type invariants.When ν is orbifold effective,explicit formulas of these invariants at degree 1 are give.This generalizes the authors’previous work for H≌Z.

关 键 词：Mahler measure Jump loci Orbifold map L^(2)-Betti number 

分 类 号：O152[理学—数学]