Domingo Toledo

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A classical theorem of great beauty describes the connection between cubic curves and hyperbolic geometry: the moduli space of the former is a quotient of the complex hyperbolic line (or real hyperbolic plane). The purpose of this paper is to exhibit a similar connection for cubic surfaces: the space of moduli is a quotient of complex hyperbolic four-space.(More)
In this paper we consider a class of systems of two coupled real scalar fields in bidimensional spacetime, with the main motivation of studying classical or linear stability of soliton solutions. Firstly, we present the class of systems and comment on the topological profile of soliton solutions one can find from the first-order equations that solve the(More)
where x = x0 0 · · ·xn+1 n+1 is a monomial of degree d and where the aL are arbitrary complex numbers, not all zero. Viewed as an equation in both the a’s and the x’s, (1.1) defines a hypersurface X in P ×Pn+1, where N +1 is the dimension of the space of homogeneous polynomials of degree d in n+ 2 variables, and where the projection p onto the first factor(More)
We show that the vector of period ratios of a cubic surface is rational over Q(ω), where ω = exp(2πi/3) if and only if the associate abelian variety is isogeneous to a product of Fermat elliptic curves. We also show how to construct cubic surfaces from a suitable totally real quintic number field K0. The ring of rational endomorphisms of the associated(More)
The moduli space of real 6-tuples in CP 1 is modeled on a quotient of hyperbolic 3-space by a nonarithmetic lattice in Isom H. This is an expository note; the first part of it is an introduction to orbifolds and hyperbolic reflection groups. These notes are an exposition of the key ideas behind our result that the moduli space Ms of stable real binary(More)