This article is cited in 15 papers

An Index Theorem for Modules on a Hypersurface Singularity

Ragnar-Olaf Buchweitz^a, Duco van Straten<sup>b

a</sup> Dept. of Computer and Mathematical Sciences, University of Toronto at Scarborough, 1265 Military Trail, Toronto, ON M1C 1A4, Canada
^b Fachbereich 17, AG Algebraische Geometrie, Johannes Gutenberg-Universität, D-55099 Mainz, Germany

Abstract: A topological interpretation of Hochster's Theta pairing of two modules on a hypersurface ring is given in terms of linking numbers. This generalizes results of M. Hochster and proves a conjecture of J. Steenbrink. As a corollary we get that the Theta pairing vanishes for isolated hypersurface singularities in an odd number of variables, as was conjectured by H. Dao.

Key words and phrases: Matrix factorisation, hypersurface singularity, maximal Cohen–Macaulay module, intersection form, linking number, K-Theory.

MSC: 32S25, 32S55, 14C17, 19D10, 19L10, 57R99

Received: March 10, 2011

Language: English

DOI: 10.17323/1609-4514-2012-12-2-237-259

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