  A general link between geometry and intermittency in passive scalar
turbulence is established. Intermittency is qualitatively traced back to events
where tracer particles stay for anomalousy long times in degenerate geometries
characterized by strong clustering. The quantitative counterpart is the
existence of special functions of particle configurations which are
statistically invariant under the flow. These are the statistical integrals of
motion controlling the scalar statistics at small scales and responsible for
the breaking of scale invariance associated to intermittency.
