Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the restriction formula   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.

23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat