Abstract
The stringy Euler number and E 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 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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