Möbius function of coordinate hyperplanes in complex ellipsoids

Abstract:

For $p_1,\dots ,p_n>0$, let $\mathbb {E}=\{z\in \mathbb {C}^n:\sum _{j=1}^n|z_j|^{2p_j}<1\}$ be a complex ellipsoid. We present effective formulas for the generalized Möbius and Green functions $m_{\mathbb {E}}(A,\cdot )$, $g_{\mathbb {E}}(A,\cdot )$ in the case where $A:=\{z\in \mathbb {E}:z_1\cdots z_k=0\}$ ($1\leq k\leq n$).