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manuscripta mathematica

, Volume 105, Issue 2, pp 143–174 | Cite as

On the string-theoretic Euler number of a class of absolutely isolated singularities

  • Dimitrios I. Dais

Abstract:

An explicit computation of the so-called string-theoretic E-function \(\) of a normal complex variety X with at most log-terminal singularities can be achieved by constructing one snc-desingularization of X, accompanied with the intersection graph of the exceptional prime divisors, and with the precise knowledge of their structure. In the present paper, it is shown that this is feasible for the case in which X is the underlying space of a class of absolutely isolated singularities (including both usual ? n -singularities and Fermat singularities of arbitrary dimension). As byproduct of the exact evaluation of \(\) lim\(\), for this class of singularities, one gets counterexamples to a conjecture of Batyrev concerning the boundedness of the string-theoretic index. Finally, the string-theoretic Euler number is also computed for global complete intersections in ℙ N with prescribed singularities of the above type.

Mathematics Subject Classification (2000): Primary 14Q15, 32S35, 32S45; Secondary 14B05, 14E15, 32S05, 32S25 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Dimitrios I. Dais
    • 1
  1. 1.Mathematics Department, Section of Algebra and Geometry, University of Ioannina, 45110 Ioannina, Greece. e-mail: ddais@cc.uoi.grGR

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