The contact polytope of the Leech lattice

The contact polytope of a lattice is the convex hull of its shortest vectors. In this paper we classify the facets of the contact polytope of the Leech lattice up to symmetry. There are 1,197,362,269,604,214,277,200 many facets in 232 orbits

Extending the Prym map to toroidal compactifications of the moduli space of abelian varieties (with an appendix by Mathieu Dutour Sikiric)

The main purpose of this paper is to present a conceptual approach to understanding the extension of the Prym map from the space of admissible double covers of stable curves to different toroidal compactifications of the moduli space of principally polarized abelian varieties. By separating the combinatorial problems from the geometric aspects we can reduce this to the computation of certain monodromy cones. In this way we not only shed new light on the extension results of Alexeev, Birkenhake, Hulek, and Vologodsky for the second Voronoi toroidal compactification, but we also apply this to other toroidal compactifications, in particular the perfect cone compactification, for which we obtain a combinatorial characterization of the indeterminacy locus, as well as a geometric description up to codimension six, and an explicit toroidal resolution of the Prym map up to codimension four. © 2017 European Mathematical Society

Relationship between productive and reproductive parameters of dairy cows in different production systems

The majority of the milk producing systems in Argentina are based on the use of perennial and annual pastures plus supplementation with cereal grains and conserved forages. The genetic change that occurred in Argentine dairy cattle was due principally to the importation of semen from the USA and Canada. In those countries the Holstein breed was selected over many years for milk yield and body size under conditions of intensive management. It has been observed that upon increasing milk producing potential as a result of genetic selection, reproductive indexes deteriorate. Under grazing conditions it is impossible to control environmental conditions to the same or nearly the same degree as in intensive systems. Therefore, the use of animals originating from intensive systems under grazing conditions results in a mismatch between the requirements of the new genotype and those that the environment can provide. Thus the increase in individual production potential could be detrimental to the overall productivity of the grazing system, since this system cannot sustain those high levels of productio