On the StringTheoretic Euler Number of a Class of Absolutely Isolated Singularities
Abstract
An explicit computation of the socalled stringtheoretic Efunction of a normal complex variety X with at most logterminal singularities can be achieved by constructing one sncdesingularization 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 A_{n}singularities and Fermat singularities of arbitrary dimension). As byproduct of the exact evaluation of e_{str}(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 stringtheoretic index. Finally, the stringtheoretic Euler number is also computed for global complete intersections in P^{N} with prescribed singularities of the above type.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 2000
 arXiv:
 arXiv:math/0011118
 Bibcode:
 2000math.....11118D
 Keywords:

 Mathematics  Algebraic Geometry;
 High Energy Physics  Theory;
 (Primary) 14Q15;
 32S35;
 32S45;
 (Secondary) 14B05;
 14E15;
 32S05;
 32S25
 EPrint:
 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