Abstract
We study the algebraic geometrical background of the Penner-Kontsevich matrix model with the potential Nα tr[− 1 2 ΛXΛX+log(1− X+ X]. We show that this model describes intersection indices of linear bundles on the discretized moduli space just in the same fashion as the Kontsevich model is related to intersection indices (cohomological classes) on Riemann surfaces of arbitrary genus. The special role of the logarithmic potential originating from the Penner matrix model is demonstrated. The boundary effects, which were not essential in the case of the Kontsevich model, are now relevant, and the intersection indices on the discretized moduli space of genus g are expressed through Kontsevich's indices of genus g and of the lower genera using a stratification procedure.
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