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| The Homology Growth for Finite Abelian Covers of Smooth Quasi-projective Varieties |
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Citation： |
Fenglin LI,Yongqiang LIU.The Homology Growth for Finite Abelian Covers of Smooth Quasi-projective Varieties[J].Chinese Annals of Mathematics B,2025,46(1):51~62 |
| Page view： 169
Net amount： 164 |
Authors： |
Fenglin LI; Yongqiang LIU |
Foundation： |
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. |
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| Abstract： |
Let X be a complex smooth quasi-projective variety with a fixed epimorphism
ν : π1(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 to ν,
known as the L2-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. |
Keywords： |
Mahler measure Jump loci Orbifold map L2-Betti number |
Classification： |
14F45, 32S20, 14H30, 57Q99 |
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