Stringy E-functions of varieties with A-D-E singularities

@article{Schepers2005StringyEO,
  title={Stringy E-functions of varieties with A-D-E singularities},
  author={Jan Schepers},
  journal={manuscripta mathematica},
  year={2005},
  volume={119},
  pages={129-157}
}
  • J. Schepers
  • Published 14 November 2005
  • Mathematics
  • manuscripta mathematica
The stringy E-function for normal irreducible complex varieties with at worst log terminal singularities was introduced by Batyrev. It is defined by data from a log resolution. If the variety is projective and Gorenstein and the stringy E-function is a polynomial, Batyrev also defined the stringy Hodge numbers as a generalization of the Hodge numbers of nonsingular projective varieties, and conjectured that they are nonnegative. We compute explicit formulae for the contribution of an A-D-E… 
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References

SHOWING 1-9 OF 9 REFERENCES
Stringy Hodge numbers of varieties with Gorenstein canonical singularities
We introduce the notion of stringy E-function for an arbitrary normal irreducible algebraic variety X with at worst log-terminal singularities. We prove some basic properties of stringy E-functions
Stringy invariants of normal surfaces
The stringy Euler number and E–function of Batyrev for log terminal singularities can in dimension 2 also be considered for a normal surface singularity with all log discrepancies nonzero in its
On the String-Theoretic Euler Number of 3-dimensional A-D-E Singularities
The string-theoretic E-functions Estr (X;u,v) of normal complex varieties X having at most log-terminal singularities are defined by means of sncresolutions. We give a direct computation of them in
Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs
Using non-Archimedian integration over spaces of arcs of algebraic varieties, we define stringy Euler numbers associated with arbitrary Kawamata log-terminal pairs. There is a natural Kawamata
On the string-theoretic Euler number of a class of absolutely isolated singularities
An explicit computation of the so-called string-theoretic E-function Estr (X; u, v) of a normal complex variety X with at most log-terminal singularities can be achieved by constructing one
Arc spaces, motivic integration and stringy invariants
The concept of motivic integration was invented by Kontsevich to show that birationally equivalent Calabi-Yau manifolds have the same Hodge numbers. He constructed a certain measure on the arc space
Principles of Algebraic Geometry
A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications
Young person''s guide to canonical singularities
A copier of the type which includes a photoreceptor on which an electrostatic latent image may be formed, a movable applicator which carries developer from a working supply of image developer and
The Hodge Characteristic, preprint
  • The Hodge Characteristic, preprint