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Ruled Exceptional Surfaces and the Poles of Motivic Zeta Functions

  Published:2007-10-01
 Printed: Oct 2007
  • B. Rodrigues
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Abstract

In this paper we study ruled surfaces which appear as an 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.
MSC Classifications: 14E15, 14J26, 14B05, 14J17, 32S45 show english descriptions Global theory and resolution of singularities [See also 14B05, 32S20, 32S45]
Rational and ruled surfaces
Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]
Singularities [See also 14B05, 14E15]
Modifications; resolution of singularities [See also 14E15]
14E15 - Global theory and resolution of singularities [See also 14B05, 32S20, 32S45]
14J26 - Rational and ruled surfaces
14B05 - Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]
14J17 - Singularities [See also 14B05, 14E15]
32S45 - Modifications; resolution of singularities [See also 14E15]
 

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