On the string-theoretic Euler number of a class of absolutely isolated singularities |
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Authors: | Dimitrios I Dais |
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Institution: | (1) Mathematics Department, Section of Algebra and Geometry, University of Ioannina, 45110 Ioannina, Greece. e-mail: ddais@cc.uoi.gr, GR |
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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 ℙℂ
N
with prescribed singularities of the above type.
Received: 2 January 2001 / Revised version: 22 May 2001 |
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Keywords: | Mathematics Subject Classification (2000): Primary 14Q15 32S35 32S45 Secondary 14B05 14E15 32S05 32S25 |
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