[en] We propose a new construction of an integrable hierarchy associated to any infinite series of Frobenius manifolds satisfying a certain stabilization condition. We study these hierarchies for Frobenius manifolds associated to A _N, D _N and B _N singularities. In the case of A _N Frobenius manifolds our hierarchy turns out to coincide with the dispersionless KP hierarchy; for B _N Frobenius manifolds it coincides with the dispersionless BKP hierarchy; and for D _N hierarchy it is a certain reduction of the dispersionless 2-component BKP hierarchy. As a side product to these results we illustrate the enumerative meaning of certain coefficients of A _N, D _N and B _N Frobenius potentials. (paper)

[en] Currently there are two proposed ansätze for NSR superstring measures: the Grushevsky ansatz and the OPSMY ansatz, which for genera g⩽4 are known to coincide. However, neither the Grushevsky nor the OPSMY ansatz leads to a vanishing two-point function in genus four, which can be constructed from the genus five expressions for the respective ansätze. This is inconsistent with the known properties of superstring amplitudes. In the present paper we show that the Grushevsky and OPSMY ansätze do not coincide in genus five. Then, by combining these ansätze, we propose a new ansatz for genus five, which now leads to a vanishing two-point function in genus four. We also show that one cannot construct an ansatz from the currently known forms in genus 6 that satisfies all known requirements for superstring measures