Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Stringy invariants of normal surfaces


Author: Willem Veys
Journal: J. Algebraic Geom. 13 (2004), 115-141
DOI: https://doi.org/10.1090/S1056-3911-03-00340-0
Published electronically: September 3, 2003
MathSciNet review: 2008717
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Abstract | References | Additional Information

Abstract: The stringy Euler number and $E$-function of Batyrev for log terminal singularities in dimension 2 can also be considered for a normal surface singularity with all log discrepancies nonzero in its minimal log resolution. Here we obtain a structure theorem for resolution graphs with respect to log discrepancies, implying that these stringy invariants can be defined in a natural way, even when some log discrepancies are zero, and more precisely for all normal surface singularities which are not log canonical. We also show that the stringy $E$-functions of log terminal surface singularities are polynomials (with rational powers) with nonnegative coefficients, yielding well defined (rationally graded) stringy Hodge numbers.


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Additional Information

Willem Veys
Affiliation: K.U.Leuven, Departement Wiskunde, Celestijnenlaan 200B, B–3001 Leuven, Belgium
Email: wim.veys@wis.kuleuven.ac.be

DOI: https://doi.org/10.1090/S1056-3911-03-00340-0
Received by editor(s): June 8, 2001
Published electronically: September 3, 2003

American Mathematical Society