On Yau sequence over complete intersection surface singularities of Brieskorn type (Q6593244)

The elliptic sequence introduced by \textit{S. S. T. Yau} [Trans. Am. Math. Soc. 257, 269--329 (1980; Zbl 0343.32009)] is one of the most powerful tools for studying elliptic normal surface singularities. To extend the methods of elliptic sequence to a broader class of singularities, \textit{T. Tomaru} [Pac. J. Math. 170, No. 1, 271--295 (1995; Zbl 0848.14017)] introduced the Yau sequence, which was further developed by \textit{K. Konno} [Asian J. Math. 16, No. 2, 279--298 (2012; Zbl 1257.14024)]. In the present paper, the author investigates the Yau sequence \(\{Z_0, \dots, Z_m\}\) for complete intersection surface singularities of Brieskorn type. The weighted dual graph, fundamental cycle, canonical cycle, and related topological invariants can be computed directly from the defining equations of the singularities as shown by \textit{K. Konno} and \textit{D. Nagashima} [Osaka J. Math. 49, No. 1, 225--245 (2012; Zbl 1246.14051)] and \textit{F.-N. Meng} and \textit{T. Okuma} [Kyushu J. Math. 68, No. 1, 121--137 (2014; Zbl 1291.14056)]. The author provides a formula for the minimal cycle with respect to the fundamental cycle, and a relation between \(K_i-K_{i+1}\) and \(Z_i\) under certain condition, where \(K_i\) denotes the canonical cycle on the support of \(Z_i\). These formulas are explicitly computed from the weighted dual graph.