Intersection-theoretical computations on \Mgbar

We determine necessary conditions for ample divisors in arbitrary genus as well as for very ample divisors in genus 2 and 3. We also compute the intersection numbers $\lambda^9$ and $\lambda_{g-1}^3$ in genus 4. The latter number is relevant for counting curves of higher genus on manifolds, cf. the recent work of Bershadsky et al.Comment: 13 pages, no figures. To appear in "Parameter Spaces", Banach Center Publications, volume in preparation. plain te

Linear orbits of arbitrary plane curves

The `linear orbit' of a plane curve of degree $d$ is its orbit in $\P^{d(d+3)/2}$ under the natural action of \PGL(3). In this paper we obtain an algorithm computing the degree of the closure of the linear orbit of an arbitrary plane curve, and give explicit formulas for plane curves with irreducible singularities. The main tool is an intersection@-theoretic study of the projective normal cone of a scheme determined by the curve in the projective space $\P^8$ of $3\times 3$ matrices; this expresses the degree of the orbit closure in terms of the degrees of suitable loci related to the limits of the curve. These limits, and the degrees of the corresponding loci, have been established in previous work.Comment: 33 pages, AmS-TeX 2.

Analysts' earnings forecasts and international asset allocation

The aim of this paper is to investigate whether financial analysts’ earnings forecasts are informative from the viewpoint of allocating investments across different stock markets. Therefore we develop a country forecast indicator reflecting the analysts’ prospects for specific stock markets. The country forecast indicator is defined as the number of companies within one and the same stock market for which analysts revise their current year earnings forecast upward divided by the total number of companies for which analysts revise their current year earnings forecasts anyway. Based on the available analysts’ earnings forecasts in the Institutional Brokers Estimate System (I/E/B/S), we calculate a monthly country forecast indicator for the stock markets in Germany, France, Italy, The Netherlands, United Kingdom, and Switzerland over the period 1990 to 1994. The time-series correlations between the monthly value of the indicator and the stock market returns around the date of calculating the indicator show that stock returns rather precede than follow revisions in earnings forecasts. An investment strategy which is based on a monthly asset allocation to that stock market with the highest value of the country forecast indicator in the preceding month, gives a slight outperformance (around 3 percent excess return) compared to an equal allocation of funds to the stock markets involved.

Complete subvarieties of moduli spaces and the Prym map

We prove that in characteristic p>0 the locus of stable curves of p-rank at most f is pure of codimension g-f in the moduli space of stable curves. Then we consider the Prym map and analyze it using tautological classes. We study the locus of curves with an etale double cover of p-rank 0 in some detail. In particular, in genus 2 we obtain a formula for the number of such curves. We end with several examples illustrating our formula.Comment: 20 pages, 1 figure. Final version, to appear in J. Reine Angew. Mat

Tautological relations and the r-spin Witten conjecture

In a series of two preprints, Y.-P. Lee studied relations satisfied by all formal Gromov-Witten potentials, as defined by A. Givental. He called them "universal relations" and studied their connection with tautological relations in the cohomology ring of moduli spaces of stable curves. Building on Y.-P. Lee's work, we give a simple proof of the fact that every tautological relation gives rise to a universal relation (which was also proved by Y.-P. Lee modulo certain results announced by C. Teleman). In particular, this implies that in any semi-simple Gromov-Witten theory where arbitrary correlators can be expressed in genus 0 correlators using only tautological relations, the formal and the geometric Gromov-Witten potentials coincide. As the most important application, we show that our results suffice to deduce the statement of a 1991 Witten conjecture on r-spin structures from the results obtained by Givental for the corresponding formal Gromov-Witten potential. The conjecture in question states that certain intersection numbers on the moduli space of r-spin structures can be arranged into a power series that satisfies the r-KdV (or r-th higher Gelfand-Dikii) hierarchy of partial differential equations.Comment: 46 pages, 7 figures, A discussion of the analyticity of Gromov-Witten potentials and a more careful description of Givental's group action added in Section 5; minor changes elsewher

From optimal to practical safety standards for dike-ring areas

After the flood disaster in 1953 in the southwestern part of the Netherlands, Van Dantzig tried to solve the economic decision problem concerning the optimal height of dikes. His solution has a fixed probability of flooding after each investment (Econometrica, 1956). However, when there is economic growth, not the probability of flooding but the expected yearly loss by flooding is the key variable in the real optimal safety strategy. Under some conditions, it is optimal to keep this expected loss within a constant interval. Therefore, when the potential damage increases by economic growth, the flooding probability has to decline in the course of time in order to keep the expected loss between the fixed boundaries. The purpose of the paper is to show the implications of the optimal solution in case there are differences between costs and benefits among dike-ring areas. Further, the paper focuses on the translation of the theoretical results into new legal standards that can work well in practice. Cost benefit analysis, optimal height of dikes, optimal safety standards.