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arXiv · 1708.02930

Lefschetz decompositions for eigenforms on a K\"ahler manifold

Donu Arapura
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Abstract

We show that the eigenspaces of the Laplacian $\Delta_k$ on $k$-forms on a compact K\"ahler manifold carry Hodge and Lefschetz decompositions. Among other consequences, we show that the positive part of the spectrum of $\Delta_k$ lies in the spectrum of $\Delta_{k+1}$.

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Donu Arapura. 2017-08-09. Lefschetz decompositions for eigenforms on a K\"ahler manifold. https://arxiv.org/abs/1708.02930

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