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Stringy invariants of normal surfaces

Willem Veys
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Abstract

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 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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Willem Veys. 2002-05-28. Stringy invariants of normal surfaces. https://arxiv.org/abs/math/0205293

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