We calculate the cycle class of the Hurwitz divisor D2 on Mg for g = 2k given by the degree k+1 covers of P with simple ramification points, two of which lie in the same fibre. We also study some aspects of the geometry of the natural map from the Hurwitz space H2k,k+1 to the moduli space M2k .

The authors give several new (and potentially useful) relationships between the multiple Gamma functions and other mathematical functions and constants. As by-products of some of these relationships, a classical de nite integral due to Euler and other de nite integrals are also considered together with closed-form evaluations of some series involving the Riemann and Hurwitz Zeta functions.

Solutions to the Riemann-Hilbert problems with irregular singularities naturally associated to semisimple Frobenius manifold structures on Hurwitz spaces (moduli spaces of meromorphic functions on Riemann surfaces) are constructed. The solutions are given in terms of meromorphic bidifferentials defined on the underlying Riemann surface. The relationship between different classes of Frobenius ma...

It is a classical result that flat coordinates for a Hurwitz Frobenius manifold can be obtained as periods of a differential along cycles on the domain curve. We generalise this construction to primary invariants of the Hurwitz Frobenius manifolds. We show that they can be obtained as periods of multidifferentials along the same cycles. The multidifferentials are obtained via the topological re...

We use algebraic methods to compute the simple Hurwitz numbers for arbitrary source and target Riemann surfaces. For an elliptic curve target, we reproduce the results previously obtained by string theorists. Motivated by the Gromov-Witten potentials, we find a general generating function for the simple Hurwitz numbers in terms of the representation theory of the symmetric group Sn. We also fin...

We calculate the cycle class of the Hurwitz divisor D2 on Mg for g = 2k given by the degree k+1 covers of P with simple ramification points, two of which lie in the same fibre. We also study some aspects of the geometry of the natural map from the Hurwitz space H2k,k+1 to the moduli space M2k .

Abslrocr -Suppose that a rational function Z ( s ) is defined by a Laurent .series, the coefficients of which are known. Several criteria are given in terms of these coefficients (the Markov parameters of Z(s)) to ensure that Re Z ( j w ) > 0 for all red w. The criteria are defined by using a Cauchy index formulation of the ratio of two rational functions, and they are of three types-involving ...

Self-dual 2-forms in D = 2n dimensions are characterised by an eigenvalue criterion. The equivalence of various definitions of selfduality is proven. We show that the self-dual 2-forms determine a n − n + 1 dimensional manifold S2n and the dimension of the maximal linear subspaces of S2n is equal to the Radon-Hurwitz number of linearly independent vector fields on the sphere S. The relation bet...

In this paper we study the reduction of Galois covers of curves, from characteristic zero to positive characteristic. The starting point is a recent result of Raynaud, which gives a criterion for good reduction for covers of the projective line branched at three points. We use the ideas of Raynaud to study the case of covers of the projective line branched at four points. Under some condition o...

This is an interesting paper that addresses some important problems in computer experiments. Our discussion will focus on the first part of the paper, namely, modeling computer experiments with tunable precision. Since the proposed EQI criterion depends on the estimation of the model parameters, we consider a general setting for the proposed model. The kriging meta models in Section 2.3 of Pich...