Journal of Algebraic Geometry

Author(s): Willem Veys
Journal: J. Algebraic Geom. 13 (2004), 115-141.
Posted: September 3, 2003
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Abstract: The stringy Euler number and

-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

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

PII: S 1056-3911(03)00340-0
Received by editor(s): June 8, 2001
Posted: September 3, 2003

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