On the restriction formula

2021/01/20 by Meng, Xiankui, Zhou, Xiangyu · 1 citation
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2101.08120

Abstract

Let φ be a quasi-psh function on a complex manifold X and let S⊂ X be a complex submanifold. Then the multiplier ideal sheaves I(φ|_S)\subsetI(φ)|_S and the complex singularity exponents c_x(φ|_S)\leqslant c_x(φ) by Ohsawa-Takegoshi L² 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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