On the string-theoretic Euler number of a class of absolutely isolated singularities
| Autor: | Dimitrios I. Dais |
|---|---|
| Rok vydání: | 2001 |
| Předmět: |
High Energy Physics - Theory
Pure mathematics Conjecture General Mathematics FOS: Physical sciences Algebraic geometry Intersection graph Algebra Mathematics - Algebraic Geometry symbols.namesake Number theory (Primary) 14Q15 32S35 32S45 High Energy Physics - Theory (hep-th) (Secondary) 14B05 14E15 32S05 32S25 FOS: Mathematics symbols Gravitational singularity Variety (universal algebra) Algebraic Geometry (math.AG) Euler number Counterexample Mathematics |
| Zdroj: | manuscripta mathematica. 105:143-174 |
| ISSN: | 0025-2611 |
| DOI: | 10.1007/pl00005875 |
| Popis: | 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 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 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. Comment: 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 |
| Databáze: | OpenAIRE |
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