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Mosc. Math. J., 2012, Volume 12, Number 2, Pages 237–259 (Mi mmj464)  

This article is cited in 12 scientific papers (total in 12 papers)

An Index Theorem for Modules on a Hypersurface Singularity

Ragnar-Olaf Buchweitza, Duco van Stratenb

a 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.

DOI: https://doi.org/10.17323/1609-4514-2012-12-2-237-259

Full text: http://www.ams.org/.../abst12-2-2012.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 32S25, 32S55, 14C17, 19D10, 19L10, 57R99
Received: March 10, 2011
Language:

Citation: Ragnar-Olaf Buchweitz, Duco van Straten, “An Index Theorem for Modules on a Hypersurface Singularity”, Mosc. Math. J., 12:2 (2012), 237–259

Citation in format AMSBIB
\Bibitem{BucVan12}
\by Ragnar-Olaf~Buchweitz, Duco~van Straten
\paper An Index Theorem for Modules on a Hypersurface Singularity
\jour Mosc. Math.~J.
\yr 2012
\vol 12
\issue 2
\pages 237--259
\mathnet{http://mi.mathnet.ru/mmj464}
\crossref{https://doi.org/10.17323/1609-4514-2012-12-2-237-259}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2978754}
\zmath{https://zbmath.org/?q=an:06126171}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000309365900002}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Polishchuk A., “Lefschetz Type Formulas for Dg-Categories”, Sel. Math.-New Ser., 20:3 (2014), 885–928  crossref  mathscinet  zmath  isi  scopus
    2. Dao H., Kurano K., “Hochster'S Theta Pairing and Numerical Equivalence”, J. K-Theory, 14:3 (2014), 495–525  crossref  mathscinet  zmath  isi  scopus
    3. Celikbas O., Iyengar S.B., Piepmeyer G., Wiegand R., “Criteria For Vanishing of Tor Over Complete Intersections”, Pac. J. Math., 276:1 (2015), 93–115  crossref  mathscinet  zmath  isi  scopus
    4. Celikbas O., Wiegand R., “Vanishing of Tor, and Why We Care About It”, J. Pure Appl. Algebr., 219:3, SI (2015), 429–448  crossref  mathscinet  zmath  isi  scopus
    5. Carqueville N., Murfet D., “a Toolkit For Defect Computations in Landau-Ginzburg Models”, String-Math 2012, Proceedings of Symposia in Pure Mathematics, 90, eds. Donagi R., Katz S., Klemm A., Morrison D., Amer Mathematical Soc, 2015, 239–250  crossref  mathscinet  zmath  isi
    6. N. Carqueville, D. Murfet, “Adjunctions and defects in Landau–Ginzburg models”, Adv. Math., 289 (2016), 480–566  crossref  mathscinet  zmath  isi  scopus
    7. M. E. Walker, “Chern characters for twisted matrix factorizations and the vanishing of the higher Herbrand difference”, Sel. Math.-New Ser., 22:3 (2016), 1749–1791  crossref  mathscinet  zmath  isi  scopus
    8. M. Reza Rahmati, “Positivity of Hochster theta over $\mathbb{C}$”, String-Math 2014, Proceedings of Symposia in Pure Mathematics, 93, eds. V. Bouchard, C. Doran, S. Méndez-Diez, C. Quigley, Amer. Math. Soc., 2016, 353–362  crossref  mathscinet  zmath  isi
    9. M. K. Brown, “On a conjecture of Dao–Kurano”, J. Algebra, 490 (2017), 462–473  crossref  mathscinet  zmath  isi  scopus
    10. D. Erman, “Divergent series and Serre's intersection formula for graded rings”, Adv. Math., 314 (2017), 573–582  crossref  mathscinet  zmath  isi  scopus
    11. M. K. Brown, C. Miller, P. Thompson, M. E. Walker, “Adams operations on matrix factorizations”, Algebr. Number Theory, 11:9 (2017), 2165–2192  crossref  mathscinet  zmath  isi  scopus
    12. M. E. Walker, “On the vanishing of Hochster's theta invariant”, Ann. K-Theory, 2:2 (2017), 131–174  crossref  mathscinet  zmath  isi
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