Initial Complex Associated to a Jet Scheme of a Determinantal Variety

We show in this paper that the principal component of the first order jet scheme over the classical determinantal variety of m x n matrices of rank at most 1 is arithmetically Cohen-Macaulay, by showing that an associated Stanley-Reisner simplicial complex is shellable.Comment: To appear in Journal of Pure and Applied Algebr

The Pre-Producers

Until its sales of a product materialize, a firm is a "pre-producer" in the market for that product. That firm may may be a new start-up, or it may already sell other products. Firms that do not succeed in generating sales eventually become discouraged and move on to other activities. When this fate befalls a lot of firms, as it recently did in several IT-related businesses, the industry experiences a "shakeout." In the model that I will present, during the shakeout some firms switch to flatter, safer earnings. This switch raises earnings at the time of the shakeout but lowers them in the long run, and it therefore raises earnings-price ratios. This has happened on the Nasdaq since March, 2000 when the Nasdaq shakeout began.

Bubbles in Prices of Exhaustible Resources

Aside from the equilibrium that Hotelling (1931) displayed, his model of non-renewable resources also contains a continuum of bubble equilibria. In all the equilibria the price of the resource rises at the rate of interest. In a bubble equilibrium, however, the consumption of the resource peters out, and a positive fraction of the original stock continues to trade forever. And that may well be happening in the market for high-end Bordeaux wines.