Vanishing of principal value integrals on surfaces
arXiv:math/0604221
Abstract
Principal value integrals are associated to multi-valued rational differential forms with normal crossings support on a non-singular algebraic variety. We prove their vanishing on rational surfaces in the context of a conjecture of Denef-Jacobs. As an application we obtain a strong vanishing result for candidate poles of p-adic and motivic Igusa zeta functions.
20 pages, to appear in J. Reine Angew. Math