Möbius function of coordinate hyperplanes in complex ellipsoids

Abstract

For $p_1,...,p_n>0$, 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 $A:=\{z\in \mathbb{E}:z_1\cdot ...\cdot z_k=0\}$ ($1\le k\le n$).

9 pages