@article{He_2024, title={Analyticity theorems for parameter-dependent plurisubharmonic functions}, volume={130}, url={https://www.mscand.dk/article/view/143441}, DOI={10.7146/math.scand.a-143441}, abstractNote={<p>In this paper, we first show that a union of upper-level sets associated to fibrewise Lelong numbers of plurisubharmonic functions is in general a pluripolar subset. Then we obtain analyticity theorems for a union of sub-level sets associated to fibrewise complex singularity exponents of some special (quasi-)plurisubharmonic functions. As a corollary, we confirm that, under certain conditions, the logarithmic poles of relative Bergman kernels form an analytic subset when the (quasi-)plurisubharmonic weight function has analytic singularities. In the end, we give counterexamples to show that the aforementioned sets are in general non-analytic even if the plurisubharmonic function is supposed to be continuous.</p>}, number={2}, journal={MATHEMATICA SCANDINAVICA}, author={He, Bojie}, year={2024}, month={May} }