We prove that Hori-Vafa mirror models for smooth Fano complete intersections in weighted projective spaces admit an interpretation as Laurent polynomials.

Let ${ℳ}_0^{ℝ}$ be the moduli space of smooth real cubic surfaces. We show that each of its components admits a real hyperbolic structure. More precisely, one can remove some lower-dimensional geodesic subspaces from a real hyperbolic space $H^4$ and form the quotient by an arithmetic group to obtain an orbifold isomorphic to a component of the moduli space. There are five components. For each we describe the corresponding lattices in $\mathrm{PO}(4,1)$. We also derive several new and several old results on the topology of ${ℳ}_0^{ℝ}$....

Etant donnés $A_1,\cdots ,A_s$ ($s\ge 3$) des $S{L}_2\left(ℂ\right)$-modules non triviaux de dimensions respectives $n_1+1\ge \cdots \ge n_s+1$ (avec $n_1=n_2+\cdots +n_s$) et $\phi \in ℒ(A_2\otimes \cdots \otimes A_s,A_1^{*})$ un $S{L}_2\left(ℂ\right)$-homomorphisme, nous montrons que l’hyperdéterminant de $\phi$ est nul sauf si les modules $A_i$ sont irréductibles et si l’homomorphisme est la multiplication des polynômes homogènes à deux variables.