Geodesic
Ruled Exceptional Surfaces and the Poles of Motivic Zeta Functions
Canadian journal of mathematics, Tome 59 (2007) no. 5, pp. 1098-1120

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In this paper we study ruled surfaces which appear as exceptional surface in a succession of blowing-ups. In particular we prove that the $e$ -invariant of such a ruled exceptional surface $E$ is strictly positive whenever its intersection with the other exceptional surfaces does not contain a fiber (of $E$ ). This fact immediately enables us to resolve an open problem concerning an intersection configuration on such a ruled exceptional surface consisting of three nonintersecting sections. In the second part of the paper we apply the non-vanishing of $e$ to the study of the poles of the well-known topological, Hodge and motivic zeta functions.
DOI : 10.4153/CJM-2007-047-2
Mots-clés : 14E15, 14J26, 14B05, 14J17, 32S45 
Rodrigues, B. Ruled Exceptional Surfaces and the Poles of Motivic Zeta Functions. Canadian journal of mathematics, Tome 59 (2007) no. 5, pp. 1098-1120. doi: 10.4153/CJM-2007-047-2
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