TY - JOUR
AU - He, Bojie
PY - 2024/05/27
Y2 - 2024/07/21
TI - Analyticity theorems for parameter-dependent plurisubharmonic functions
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 130
IS - 2
SE - Articles
DO - 10.7146/math.scand.a-143441
UR - https://www.mscand.dk/article/view/143441
SP -
AB - <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>
ER -