The Abel map for surface singularities II. Generic analytic structure

On the topology of elliptic singularities

“…First we recall the construction of the sequence in the general (not necessarily numerically Gorenstein) case according to S. S.-T. Yau, and we list several properties what we will need. Later we will provide another elliptic sequence in the non-numerically Gorenstein case, which was introduced in [NN18], whose definition 'adapts' the numerically Gorenstein case. The length of both sequences serve as upper bounds for the geometric genus of any analytic structure supported on the topological type identified by the graph.…”

“…The length of both sequences serve as upper bounds for the geometric genus of any analytic structure supported on the topological type identified by the graph. The sequence from [NN18] differs from the one introduced by Yau, however, our goal is to prove that their length is the same.…”

“…3.4. The elliptic sequence in the non-numerically Gorenstein case, according to [NN18]. Assume that Z K ∈ L, that is, r [ZK ] = 0.…”

“…C m }. (c) [NN18] The support of any numerically Gorenstein connected subgraph belongs to {B i } m i=0 .…”

“…In order to eliminate these difficulties, we consider a new elliptic sequence, which in the nonnumerically Gorenstein case is different than the one studied by Yau, and which fits much better in such comparisons. It was motivated (and introduced) in the author's study of the Abel map of surface singularities [NN18], and it has several advantages compared with the earlier approaches. E.g., it identifies the support of a numerically Gorenstein subgraph with the following property.…”