Hodge Number of Cohomology of Local Systems on the Complement of Hyperplanes in $Bbb P^3$

Journal of Mathematical Sciences

Kawahara, Yukihito¹ 

关键词: Hodge structure;    cohomology of local system;    arrangement of hyperplanes;    Kummer covering;    Euler characteristic;    blowing up;    logarithmic form;    Chow group;    Chern class;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

ThecohomologyofthelocalsystemonthecomplementofhyperplaneshasaHodgestructureasthe$α$-invariantcohomologyofaKummercoveringramifiedalongtheirhyperplanesforagenericcharacter$α$.Inthispaperwestudythecaseofarrangementsofhyperplanesinthethreedimensionalcomplexprojectivespace.WeconstructaresolutionforanarrangementofhyperplanesandcomputeitsChowgroup.BycomputingthefirstChernclassoflogarithmic1-forms,wecanobtaintheEulercharacteristicandtheHodgenumbersofcohomologyoflocalsystemsusingtheintersectionsetofthearrangementofhyperplanesandbinomialcoefficients.

【 授权许可】

Unknown