Reduced classes and curve counting on surfaces II: calculations

We calculate the stable pair theory of a projective surface $S$. For fixed curve class $\beta\in H^2(S)$ the results are entirely topological, depending on $\beta^2$, $\beta.c_1(S)$, $c_1(S)^2$, $c_2(S)$, $b_1(S)$ \emph{and} invariants of the ring structure on $H^*(S)$ such as the Pfaffian of $\beta$ considered as an element of $\Lambda^2 H^1(S)^*$. Amongst other things, this proves an extension of the G\"ottsche conjecture to non-ample linear systems. We also give conditions under which this calculates the full 3-fold reduced residue theory of $K_S$. This is related to the reduced residue Gromov-Witten theory of $S$ via the MNOP conjecture. When the surface has no holomorphic 2-forms this can be expressed as saying that certain Gromov-Witten invariants of $S$ are topological. Our method uses the results of \cite{KT1} to express the reduced virtual cycle in terms of Euler classes of bundles over a natural smooth ambient space.Comment: 19 pages. Minor correction

Stable pair invariants of surfaces and Seiberg-Witten invariants

The moduli space of stable pairs on a local surface $X=K_S$ is in general non-compact. The action of $\mathbb{C}^*$ on the fibres of $X$ induces an action on the moduli space and the stable pair invariants of $X$ are defined by the virtual localization formula. We study the contribution to these invariants of stable pairs (scheme theoretically) supported in the zero section $S \subset X$. Sometimes there are no other contributions, e.g. when the curve class $\beta$ is irreducible. We relate these surface stable pair invariants to the Poincar\'e invariants of D\"urr-Kabanov-Okonek. The latter are equal to the Seiberg-Witten invariants of $S$ by work of D\"urr-Kabanov-Okonek and Chang-Kiem. We give two applications of our result. (1) For irreducible curve classes the GW/PT correspondence for $X = K_S$ implies Taubes' GW/SW correspondence for $S$. (2) When $p_g(S) = 0$, the difference of surface stable pair invariants in class $\beta$ and $K_S - \beta$ is a universal topological expression.Comment: 25 pages. Published version. Content the same. Exposition completely changed following referee's suggestion

A note on the expectations hypothesis at the founding of the Fed

One of the most influential tests of the expectations hypothesis is Mankiw and Miron (1986), who found that the spread between the long-term and short-term rates provided predictive power for the short-term rate before the Fed's founding but not after. They suggested that the failure of the expectations hypothesis after the Fed's founding was due to the Fed's practice of smoothing short-term interest rates. We show that their finding that the expectations hypothesis fares better prior to the Fed's founding is due to the fact that the test they employ tends to generate results that are more favorable to the expectations hypothesis during periods when there is extreme volatility in the short-term rate. (Earlier version titled: The expectations theory and the founding of the Fed: another look at the evidence)Interest rates ; Rational expectations (Economic theory) ; Federal Reserve System - History

Dutch corporate liquidity mangement: New evidence on aggregation

In this paper we investigate Dutch corporate liquidity management in general, and target adjustment behaviour in particular. To this purpose, we use a simple error correction model of corporate liquidity holdings applied to firm-level data for the period 1977-1997. We confirm the existence of long-run liquidity targets at the firm level. We also find that changes in liquidity holdings are driven by short-run shocks as well as the urge to converge towards targeted liquidity levels. The rate of target convergence is higher when we include more firm-specific information in the target. This result supports the idea that increased precision in defining liquidity targets associates with a faster observed rate of target convergence. It also suggests that the slow speeds of adjustment obtained in many macro studies on money demand are artefacts of aggregation bias.corporate liquidity demand, precautionary liquidity

Industries and the bank lending effects of bank credit demand and monetary policy in Germany

This paper presents evidence on the industry effects of bank lending in Germany and identifies the industry effects of bank lending associated with changes in monetary policy and industryspecific bank credit demand. To this end, we estimate individual bank lending functions for 13 manufacturing and non-manufacturing industries and five banking groups using quarterly bank balance sheet and bank lending data for the period 1992:1-2002:4. The evidence from dynamic panel data models shows that industry-specific bank lending growth predominantly responds to changes in industry-specific bank credit demand rather than to changes in monetary policy. In fact, conclusions regarding the bank lending effects of monetary policy are very sensitive to the choice of industry. The empirical results lend strong support to the existence of industry effects of bank lending. Because industries are a prominent source of variation in the bank lending effects of bank credit demand and monetary policy, the paper concludes that the industry composition of bank credit portfolios is an important determinant of bank lending growth and monetary policy effectiveness. --Monetary policy transmission,credit channel,industry structure,dynamic panel data

Virtual Segre and Verlinde numbers of projective surfaces

Recently, Marian-Oprea-Pandharipande established (a generalization of) Lehn's conjecture for Segre numbers associated to Hilbert schemes of points on surfaces. Extending work of Johnson, they provided a conjectural correspondence between Segre and Verlinde numbers. For surfaces with holomorphic 2-form, we propose conjectural generalizations of their results to moduli spaces of stable sheaves of any rank. Using Mochizuki's formula, we derive a universal function which expresses virtual Segre and Verlinde numbers of surfaces with holomorphic 2-form in terms of Seiberg-Witten invariants and intersection numbers on products of Hilbert schemes of points. We prove that certain canonical virtual Segre and Verlinde numbers of general type surfaces are topological invariants and we verify our conjectures in examples. The power series in our conjectures are algebraic functions, for which we find expressions in several cases and which are permuted under certain Galois actions. Our conjectures imply an algebraic analog of the Mari\~{n}o-Moore conjecture for higher rank Donaldson invariants. For ranks $3$ and $4$, we obtain new expressions for Donaldson invariants in terms of Seiberg-Witten invariants.Comment: Minor corrections. 38 page