A note on Abelian varieties embedded in quadrics

We show that if A is a d-dimensional abelian variety in a smooth quadric of dimension 2d then d=1 and A is an elliptic curve of bidegree (2,2) on a quadric. This extends a result of Van de Ven which says that A only can be embedded in P^{2d} when d=1 or 2.Comment: 5 page

Who does the chores? Estimation of a household production function in Peru

In less developed countries like Peru, it is very frequent to observe that, in poor households, parents and children work together doing household work in their own home. This fact is even more evident among girls, who work at home cleaning, cooking, taking care of younger siblings, etc., which may deter them from attending school. In the current literature on child labour, it is always assumed that this occurs because girls are more productive at home than boys; therefore is more likely to observe girls staying home and boys working in the labour market. To check to what extent this common assumption is true, this paper estimates the determinants of household work in Peru, and obtains the parameters of the production function of “chores”. Since the total amount of “chores” is not observable, I use wages and the first order conditions of a standard time allocation model to estimate the model. The estimated production function is consistent with a strictly concave production function in which the inputs are substitutes. It also shows that girls have a higher marginal product than boys in the production of “chores”. All data was taken from the Peruvian Living Standard Measurement Survey of 1997 and 2000.time allocation, household work, child labor

Reduction of Almost Poisson brackets and Hamiltonization of the Chaplygin Sphere

We construct different almost Poisson brackets for nonholonomic systems than those existing in the literature and study their reduction. Such brackets are built by considering non-canonical two-forms on the cotangent bundle of configuration space and then carrying out a projection onto the constraint space that encodes the Lagrange-D'Alembert principle. We justify the need for this type of brackets by working out the reduction of the celebrated Chaplygin sphere rolling problem. Our construction provides a geometric explanation of the Hamiltonization of the problem given by A. V. Borisov and I. S. Mamaev