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arXiv · 2501.04232

Remarks on the Direct Image Sheaf of Logarithmic Pluricanonical Bundles and the Non-Vanishing Conjecture

Houari Benammar Ammar
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Abstract

By applying the Chen-Jiang decomposition, we prove that the non-vanishing conjecture holds for an lc pair \((X, \Delta)\), where \(X\) is an irregular variety, provided it holds for lower-dimensional varieties. In the second part, we extend the Catanese-Fujita-Kawamata decomposition to the klt case \((X, \Delta)\), which leads to the existence of sections of \(K_X + \Delta\) in certain situations.

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Houari Benammar Ammar. 2025-01-08. Remarks on the Direct Image Sheaf of Logarithmic Pluricanonical Bundles and the Non-Vanishing Conjecture. https://arxiv.org/abs/2501.04232

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