2000/11/30 by Dimitrios I. Dais
Mathematics · Physics and Astronomy · #math.AG #hep-th #msc:14Q15 #msc:32S35 #msc:32S45 #msc:14B05 #msc:14E15 #msc:32S05 #msc:32S25
published as manuscripta mathematica 105 (2001) 2, 143-174 · LateX 2e, 27 pages, 4 eps figures. Revised version V2 (October 2001) corrects some arithmetical inaccuracies (pointed out by N. Kakimi, concering the discrepancy coefficients) of V1, and minor misprints of the published version
arxiv created 2001/10/26 · arxiv updated 2009/11/30
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 An-singularities and Fermat singularities of arbitrary dimension). As byproduct of the exact evaluation of estr(X), for this class of singularities, one gets (in contrast to the expectations of V1!) 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 PN with prescribed singularities of the above type.