Némethi, András; Sigurdsson, Baldur The geometric genus of hypersurface singularities. (English) Zbl 1343.32020 J. Eur. Math. Soc. (JEMS) 18, No. 4, 825-851 (2016). Let \((X,0)\) be a normal surface singularity whose link \(M\) is a rational homology sphere. A path is a sequence of integral cycles supported on the exceptional curve of a fixed resolution, at each step increasing only by a base element, and connecting the trivial cycle to the anticanonical cycle. For such a path \(\gamma\), a path lattice cohomology \(\mathbb{H}^0(\gamma)\) is defined as well as its normalized rank \(eu(\mathbb{H}^0(\gamma))\). It is proved that \(p_g=\underset{\gamma}{\min}\;eu (\mathbb{H}^0(\gamma))\) in the following cases: (a) for super isolated singularities; (b) for singularities with non-degenerate Newton principal part; (c) if \(\mathbb{H}^q(M)=0\) for \(q\geq 1\) and the singular germ satisfies the so-called SWIC Conjecture (in particular, for all weighted homogeneous and minimally elliptic singularities). Reviewer: Gerhard Pfister (Kaiserslautern) Cited in 5 Documents MSC: 32S05 Local complex singularities 32S25 Complex surface and hypersurface singularities 32S50 Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants 14B05 Singularities in algebraic geometry Keywords:normal surface singularities; hypersurface singularities; links of singularities; Newton non-degenerate singularities; geometric genus PDFBibTeX XMLCite \textit{A. Némethi} and \textit{B. Sigurdsson}, J. Eur. Math. Soc. (JEMS) 18, No. 4, 825--851 (2016; Zbl 1343.32020) Full Text: DOI arXiv References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.