Abstract
AbstractThis chapter has three parts. The first one presents rational singularities: the geometric genus of these germs vanishes. We provide several of their topological characterisations, and we list several key examples as well. Then we examine elliptic singularities. We start with Kulikov and minimally elliptic germs, but then we discuss the general (weakly) elliptic cases as well. We define elliptic sequences, and we examine their role in the topological and analytical classifications. We compute several invariants (e.g., Hilbert-Samuel function, geometric genus). The last part is devoted to ‘weighted cubes’. This is a preparatory part for the lattice cohomology chapter. Here we prove all the homotopical statements, which will guarantee that the lattice cohomology is a well-defined cohomology theory. For this we need to prove several homotopy equivalences, in the homotopy retractions the guiding combinatorial objects are the generalized versions of the computation sequences of Laufer.
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