Links and analytic invariants of superisolated singularities

Luengo-Velasco, I.; Melle-Hernández, A.; Némethi, A.

doi:10.1090/S1056-3911-05-00397-8

Authors: I. Luengo-Velasco, A. Melle-Hernández and A. Némethi
Journal: J. Algebraic Geom. 14 (2005), 543-565
DOI: https://doi.org/10.1090/S1056-3911-05-00397-8
Published electronically: March 24, 2005
MathSciNet review: 2129010
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Abstract | References | Additional Information

Abstract: 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.

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Additional Information

I. Luengo-Velasco
Affiliation: Facultad de Matemáticas, Universidad Complutense, Plaza de Ciencias, E-28040, Madrid, Spain
Email: iluengo@mat.ucm.es

A. Melle-Hernández
Affiliation: Department of Mathematics, Ohio State University, Columbus, Ohio 43210
Email: amelle@mat.ucm.es

A. Némethi
Affiliation: Rényi Institute of Mathematics, Budapest, Hungary
Email: nemethi@math.ohio-state.edu, nemethi@renyi.hu

Received by editor(s): March 29, 2004
Received by editor(s) in revised form: June 19, 2004
Published electronically: March 24, 2005
Additional Notes: The first two authors are partially supported by BFM2001-1488-C02-01. The third author is partially supported by NSF grant DMS-0304759.