Ratio methods to the mean estimation with known quantiles

We address the problem of estimating the finite population mean in survey sampling, by exploiting any available auxiliary information in order to increase the precision of classical estimators. The idea is to use any population quantiles of the available auxiliary variables which are known in many real situation from census, administrative files, etc. This is achieved using these known quantities in the construction of the estimators, by modifying the usual ratio estimation methods and afterwards defining a general class of exponentiation ratio estimators. The advantages of the proposed estimators are demonstrated using theoretical asymptotic tools and through a simulation study.     

On the 0-dimensional irreducible components of the singular locus of \mathcal{A}_g

In this short note we give a characterization of extremal principally polarized abelian varieties determining an isolated point in Sing The case g = 5 is treated in depth.Received: 14 June 2004     

A pencil in with three points at the boundary

We construct a linear pencilC _t of curves in , such that for eacht ∈ ℙ₁, Aut(C _t) contains the alternating group and we describe the curves of the pencil contained on the boundary of . Partially supported by FONDECYT Grant No. 0995-90.     

A robust and hierarchical approach for the automatic co-registration of intensity and visible images

This paper presents a new robust approach to integrate intensity and visible images which have been acquired with a terrestrial laser scanner and a calibrated digital camera, respectively. In particular, an automatic and hierarchical method for the co-registration of both sensors is developed. The approach integrates several existing solutions to improve the performance of the co-registration between range-based and visible images: the Affine Scale-Invariant Feature Transform (A-SIFT), the epipolar geometry, the collinearity equations, the Groebner basis solution and the RANdom SAmple Consensus (RANSAC), integrating a voting scheme. The approach presented herein improves the existing co-registration approaches in automation, robustness, reliability and accuracy.     

On the order of an automorphism of a smooth hypersurface

In this paper we give an effective criterion as to when a positive integer q is the order of an automorphism of a smooth hypersurface of dimension n and degree d, for every d ≥ 3, n ≥ 2, (n, d) ≠ (2, 4), and gcd(q, d) = gcd(q, d ? 1) = 1. This allows us to give a complete criterion in the case where q = p is a prime number. In particular, we show the following result: If X is a smooth hypersurface of dimension n and degree d admitting an automorphism of prime order p then p < (d ? 1) ⁿ⁺¹; and if p > (d ? 1) ⁿ then X is isomorphic to the Klein hypersurface, n = 2 or n + 2 is prime, and p = Φ _n+2(1 ? d) where Φ _n+2 is the (n+2)-th cyclotomic polynomial. Finally, we provide some applications to intermediate jacobians of Klein hypersurfaces.     

Families of irreducible principally polarized abelian varieties isomorphic to a product of elliptic curves

For each greater than or equal to two, we give a family of
-dimensional, irreducible principally polarized abelian varieties isomorphic to a product of elliptic curves. This family corresponds to the modular curve .

     

Automorphisms of prime order of smooth cubic <Emphasis Type="Italic">n</Emphasis>-folds

In this paper we give an effective criterion as to when a prime number p is the order of an automorphism of a smooth cubic hypersurface of \({\mathbb{P}^{n+1}}\), for a fixed n ≥ 2. We also provide a computational method to classify all such hypersurfaces that admit an automorphism of prime order p. In particular, we show that p < 2 ⁿ⁺¹ and that any such hypersurface admitting an automorphism of order p > 2 ⁿ is isomorphic to the Klein n-fold. We apply our method to compute exhaustive lists of automorphism of prime order of smooth cubic threefolds and fourfolds. Finally, we provide an application to the moduli space of principally polarized abelian varieties.