By using superisolated surface singularities whose link is a rational
homology sphere we give counterexamples to some of the most important
conjetures concernig invariants of normal surface singularities.Comment: Revised version, to appear in Journal of Algebraic Geometr

Luengo-Velasco, I.

Melle-Hernandez, A.

Nemethi, A.

English

arXiv

Using superisolated singularities we present examples and counterexamples to some of the most important conjectures regarding invariants of normal surface singularities. More precisely, we show that the “Seiberg-Witten invariant conjecture”(of Nicolaescu and the third author), the “Universal abelian cover conjecture” (of Neumann and Wahl) and the “Geometric genus conjecture” fail (at least at that generality in which they were formulated). Moreover, we also show that for Gorenstein singularities (even with integral homology sphere links) besides the geometric genus, the embedded dimension and the multiplicity (in particular, the Hilbert-Samuel function) also fail to be topological; and in general, the Artin cycle does not coincide with the maximal (ideal) cycle.</p

Links and analytic invariants of superisolated singularities

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