On the restriction formula

Xiankui Meng; Xiangyu Zhou

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arXiv · 2101.08120

On the restriction formula

Xiankui Meng·Xiangyu Zhou

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Abstract

Let $\varphi$ be a quasi-psh function on a complex manifold $X$ and let $S\subset X$ be a complex submanifold. Then the multiplier ideal sheaves $\mathcal{I}(\varphi|_S)\subset\mathcal{I}(\varphi)|_{S}$ and the complex singularity exponents $c_{x}\left(\varphi|_{S}\right)\leqslant c_{x}(\varphi)$ by Ohsawa-Takegoshi $L^{2}$ extension theorem. An interesting question is to know whether it is possible to get equalities in the above formulas. In the present article, we show that the answer is positive when $S$ is chosen outside a measure zero set in a suitable projective space.

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Xiankui Meng, Xiangyu Zhou. 2021-01-20. On the restriction formula. https://arxiv.org/abs/2101.08120

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