Algebraic Integrability of Foliations of the Plane

We give an algorithm to decide whether an algebraic plane foliation F has a rational first integral and to compute it in the affirmative case. The algorithm runs whenever we assume the polyhedrality of the cone of curves of the surface obtained after blowing-up the set B_F of infinitely near points needed to get the dicritical exceptional divisors of a minimal resolution of the singularities of F. This condition can be detected in several ways, one of them from the proximity relations in B_F and, as a particular case, it holds when the cardinality of B_F is less than 9

Generating sequences and Poincar\'e series for a finite set of plane divisorial valuations

Let $V$ be a finite set of divisorial valuations centered at a 2-dimensional regular local ring $R$. In this paper we study its structure by means of the semigroup of values, $S_V$, and the multi-index graded algebra defined by $V$, \gr_V R. We prove that $S_V$ is finitely generated and we compute its minimal set of generators following the study of reduced curve singularities. Moreover, we prove a unique decomposition theorem for the elements of the semigroup. The comparison between valuations in $V$, the approximation of a reduced plane curve singularity $C$ by families of sets $V^{(k)}$ of divisorial valuations, and the relationship between the value semigroup of $C$ and the semigroups of the sets $V^{(k)}$, allow us to obtain the (finite) minimal generating sequences for $C$ as well as for $V$. We also analyze the structure of the homogeneous components of \gr_V R. The study of their dimensions allows us to relate the Poincar\'e series for $V$ and for a general curve $C$ of $V$. Since the last series coincides with the Alexander polynomial of the singularity, we can deduce a formula of A'Campo type for the Poincar\'e series of $V$. Moreover, the Poincar\'e series of $C$ could be seen as the limit of the series of $V^{(k)}$, $k\ge 0$

Second thoughts on second moments : panel evidence on asset-based models of currency crises

The literature on speculative attacks has been given new impetus by the collapse of the European currency arrangements beginning in 1992, by the Mexican peso crisis and after-effects in 1994, and most recently by speculative attacks across Asia. One stand of this literature stresses the importance of imbalances in stocks of monetary and financial aggregates rather than traditional"flow"factors, arguing that massive, volatile capital flows have become a dominant feature of the global landscape, and that exchange-rate levels and current accounts have not proved convincing as proximate causes of crises. The authors test two popular asset-based models of speculative attacks -- Krugman and Rotemberg (1992) and Calvo and Mendoza (1995) -- especially their emphasis on the second moments of monetary aggregates. Analyzing monthly panels of appropriate countries in three regions, they find evidence for the importance of money/reserve ratios predicted by both models, and their variance as predicted by Calvo and Mendoza. But the variance of velocity does not appear to be important, casting some doubt on the Krugman-Rotemberg target zone framework and the interpretation of the Calvo-Mendoza results.Fiscal&Monetary Policy,Payment Systems&Infrastructure,Environmental Economics&Policies,Insurance&Risk Mitigation,Economic Theory&Research,Economic Theory&Research,Fiscal&Monetary Policy,Macroeconomic Management,Environmental Economics&Policies,Economic Stabilization