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Existence of oblique polar lines for the meromorphic extension of the current valued function $int |f|^{2lambda}|g|^{2mu}square$ is given under the following hypotheses: $f$ and $g$ are holomorphic function germs in $CC^{n+1}$ such that $g$ is non-singular, the germ $S:=ens{d fwedge d g =0}$ is one dimensional, and $g|_S$ is proper and finite. The main tools we use are interaction of strata for $f$ (see cite{B:91}), monodromy of the local system $H^{n-1}(u)$ on $S$ for a given eigenvalue $exp(-2ipi u)$ of the monodromy of $f$, and the monodromy of the cover $g|_S$. Two non-trivial examples are completely worked out.
Feynman integral computations in theoretical high energy particle physics frequently involve square roots in the kinematic variables. Physicists often want to solve Feynman integrals in terms of multiple polylogarithms. One way to obtain a solution i
We show some of the conjectures of Pappas and Rapoport concerning the moduli stack of $mathcal{G}$-torsors on a curve C, where $mathcal{G}$ is a semisimple Bruhat-Tits group scheme on C. In particular we prove the analog of the uniformization theorem
AKARI (formerly ASTRO-F) is an infrared space telescope designed for an all-sky survey at 10-180 (mu)m, and deep pointed surveys of selected areas at 2-180 (mu)m. The deep pointed surveys with AKARI will significantly advance our understanding of gal
We prove that for an indecomposable convergent or overconvergent F-isocrystal on a smooth irreducible variety over a perfect field of characteristic p, the gap between consecutive slopes at the generic point cannot exceed 1. (This may be thought of a
We introduce the notions of infinitesimal extension and square-zero extension in the context of simplicial commutatie algebras. We next investigate their mutual relationship and we show that the Postnikov tower of a simplicial commutative algebra is