On the invariant spectrum on

Hajli, Mounir

doi:10.1002/mana.201400172

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2018

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“…Proof. This proposition follows from [4,Proposition 3.4] We denote by ∆ n,∞ the Laplacian associated to the singular Kähler metric ω n,∞ . By Theorem 1.19, ∆ n,∞ has a non-negative, infinite and discrete spectrum.…”

Section: An Examplementioning

confidence: 98%

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The canonical spectrum of projective toric manifolds

Hajli

2018

Int. J. Math.

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Let [Formula: see text] be a complex projective toric manifold. We associated to [Formula: see text], a positive and closed [Formula: see text]-current called the canonical toric Kähler current of [Formula: see text] denoted by [Formula: see text], and a new invariant called the canonical spectrum of [Formula: see text]. This spectrum is obtained as the set of the eigenvalues of a singular Laplacian defined by [Formula: see text] and which is described uniquely by the combinatorial structure of [Formula: see text]. The construction of this Laplacian and the study of its spectral properties are the consequence of a generalized spectral theory of Laplacians on compact Kähler manifolds that we develop in this paper.

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Section: An Examplementioning

confidence: 98%

“…Examples of computation of the canonical spectrum are given in Example 2.5. Some properties of this spectrum in dimension 1 are studied in [4].…”

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confidence: 99%