Mathematical proceedings of the Cambridge Philosophical Society vol:143 pages:543-555
Inspired by p-adic (and real) principal value integrals, we introduce motivic
principal value integrals associated to multi-valued rational differential forms on smooth
algebraic varieties. We investigate the natural question whether (for complete varieties) this
notion is a birational invariant. The answer seems to be related to the dichotomy of the
Minimal Model Program.