Let Omega subset of R-n be a bounded, convex, and open set with real analytic boundary Let T-Omega subset of C-n be the tube with base Omega, and let B be the Bergman kernel of T-Omega. If Omega is strongly convex, then B is analytic away from the boundary diagonal. In the weakly convex case this is no longer true. In this situation we relate the off-diagonal points where analyticity fails to the characteristic lines. These lines are contained in the boundary of T-Omega, and they are projections of the Treves curves. These curves are symplectic invariants that are determined by the CR (Cauchy-Riemann) structure of the boundary of T-Omega. Note that Treves curves exist only when Omega has at feast one weakly convex boundary point. [References: 36]
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