- Full text PDF available (26)
- This year (1)
- Last 5 years (2)
- Last 10 years (12)
Journals and Conferences
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)
The moduli space of cubic threefolds in CP , with some minor birational modifications, is the Baily-Borel compactification of the quotient of the complex 10-ball by a discrete group. We describe both the birational modifications and the discrete group explicitly.
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)
We review some developments in rigidity theory of compact Kähler manifolds and related developments on restrictions on their possible
For a coherent analytic sheaf F on a complex manifold X and a holomorphic map ƒ : X —• Y to a complex manifold Y, with ƒ proper on the support of F, we prove a Grothendieck-Riemann-Roch formula as in  relating the Todd classes of X, Y and the Chern character of J and its direct images. This is the first example of a Riemann-Roch theorem for general… (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)
We prove that the so-called sporadic complex reeection triangle groups in SU(2; 1) are all non-arithmetic but one, and that they are not commensurable to Mostow or Picard lattices (with a small list of exceptions). This provides an innnite list of potential new non-arithmetic lattices in SU(2; 1).