5 M ay 2 00 9 UNIVERSAL RECURSIVE FORMULAE FOR Q - CURVATURES

ar X iv : 0 80 4 . 27 45 v 1 [ m at h . D G ] 1 7 A pr 2 00 8 UNIVERSAL RECURSIVE FORMULAS FOR Q - CURVATURE

We discuss recursive formulas for Branson’sQ-curvatures. The formulas present Q-curvatures of any order in terms of lower order Qcurvatures and lower order GJMS-operators. These presentations are universal in the sense that the recursive structure does not depend on the dimension of the underlying space. We give proofs for Q4 and Q6 for general metrics, and for Q8 for conformally flat metrics. ...

ar X iv : 0 80 4 . 27 45 v 2 [ m at h . D G ] 8 S ep 2 00 8 UNIVERSAL RECURSIVE FORMULAS FOR Q - CURVATURE

We discuss recursive formulas for Branson’s Q-curvatures. These formulas present Q-curvatures of any order on manifolds of even dimension in terms of lower order Q-curvatures and lower order GJMS-operators. They are universal in the sense that their formulation does not depend on the dimension of the underlying space. We introduce two algorithms of different nature for the computation of the co...

1 9 M ay 2 00 5 Lefschetz formulae for p - adic groups

ar X iv : 0 90 5 . 35 80 v 1 [ m at h . A G ] 2 1 M ay 2 00 9 Q - UNIVERSAL DESINGULARIZATION

We prove that the algorithm for desingularization of algebraic varieties in characteristic zero of the first two authors is functorial with respect to regular morphisms. For this purpose, we show that, in characteristic zero, a regular morphism with connected affine source can be factored into a smooth morphism, a ground-field extension and a generic-fibre embedding. Every variety of characteri...

ar X iv : 0 90 5 . 25 85 v 1 [ m at h . C O ] 1 5 M ay 2 00 9 CHARACTERISTIC POINTS OF RECURSIVE SYSTEMS

Characteristic points have been a primary tool in the study of a generating function defined by a single recursive equation. We investigate the proper way to adapt this tool when working with multi-equation recursive systems.