4,323 research outputs found
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 be a finite set of divisorial valuations centered at a 2-dimensional
regular local ring . In this paper we study its structure by means of the
semigroup of values, , and the multi-index graded algebra defined by ,
\gr_V R. We prove that 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 , the approximation of a reduced
plane curve singularity by families of sets of divisorial
valuations, and the relationship between the value semigroup of and the
semigroups of the sets , allow us to obtain the (finite) minimal
generating sequences for as well as for .
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 and
for a general curve of . 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 . Moreover, the Poincar\'e series of
could be seen as the limit of the series of ,
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
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