The purpose of this note is to correct a mistake in the article “A curve selection lemma in spaces of arcs and the image of the Nash map” Compositio Math. 142 (2006), 119–130. It is due to an overlooked hypothesis in the definition of generically stable subset of the space of arcs X∞ of a variety X defined over a perfect field k.

We investigate sources of economic fluctuations in Chile during 1998–2007 within the framework of a standard neoclassical growth model with time-varying frictions (wedges). We analyze the relative importance of efficiency, labor, investment, and government/trade wedges for business cycles in Chile. The purpose of this exercise is twofold: (i) focusing the policy discussion on the most important wedges in the economy and (ii) identifying which broad class of models would present fruitful avenues for further research. We find that different wedges have played different roles during our studied period, but that the efficiency, labor, and investment wedges have had the greatest impact. We also compare our results with existing studies on emerging and developed economies.

We prove that, if X is a variety over an uncountable algebraically closed field k of characteristic zero, then any irreducible exceptional divisor E on a resolution of singularities of X which is not uniruled, belongs to the image of the Nash map, i.e. corresponds to an irreducible component of the space of arcs on X centred in Sing X. This reduces the Nash problem of arcs to understanding which uniruled essential divisors are in the image of the Nash map, more generally, how to determine the uniruled essential divisors from the space of arcs.

We prove a finiteness result in the space of arcs $X_\infty$ of a singular variety X, which is an extension of the stability result of Denef and Loeser (Germs of arcs on singular algebraic varieties and motivic integration, Invent. Math. 135 (1999), 201–232). From this follows a curve selection lemma for generically stable subsets of $X_\infty$. As a consequence, we extend to all dimensions the problem of wedges, proposed by Lejeune-Jalabert (Arcs analytiques et résolution minimale des singularités des surfaces quasi-homogénes, Lecture Notes in Mathematics, vol. 777 (Springer, Berlin, 1980), 303–336), and we obtain that an affirmative answer to this problem is equivalent to the surjectivity of the Nash map. This implies, for instance, that the Nash map is bijective for sandwiched surface singularities.

Let T be a triangle. P be a parallelogram, E be an ellipse, A, B be concentric circles, C, D be concentric dartboard regions, R, S be rectangles of the same orientation, U, V be two finite unions and/or differences of convex regions in the Euclidean plane. Given a function f on [0,∞), let E[/(r), U, V] denote the mean value of f(|u–v|), where |u–v| is the distance between u∊U and v∊V. Using Borel’s overlap technique, a specific distance weight function and a specific equivalence relation, we obtain formulae expressing E[f(r), U, V] in terms of triple integrals, expressing E(rn, U, V), E[f(r), A, V] and E[f(r), R, V] in terms of double integrals, expressing E[f(r), A, B], E[f(r), R, S], E[f(r), T, T], E[f(r), P, P], E(rn, C, D) and E(rn, R, V) in terms of single integrals, and expressing E(rn, R, S), E(rn, P, P), E(rn, T, T), E(rn, E, E) in terms of elementary functions, where n is an integer ≧−1. Many other related results are also given.