Lefschetz decompositions for eigenforms on a Kähler manifold

2017/08/09 by Arapura, Donu
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1708.02930

Abstract

We show that the eigenspaces of the Laplacian Δ_k on k-forms on a compact Kähler manifold carry Hodge and Lefschetz decompositions. Among other consequences, we show that the positive part of the spectrum of Δ_k lies in the spectrum of Δ_k+1.

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