Algebraic and symplectic Gromov-Witten invariants coincide

For a complex projective manifold Gromov-Witten invariants can be constructed either algebraically or symplectically. Using the versions of Gromov-Witten theory by Behrend and Fantechi on the algebraic side and by the author on the symplectic side, we prove that both points of view give the same results. A similar statement has been obtained independently by Li and Tian using their definitions of algebraic and symplectic Gromov-Witten invariants (alg-geom/9712035).Comment: 43 pages, Latex2e with AMS-font

Logarithmic Gromov-Witten invariants

The goal of this paper is to give a general theory of logarithmic Gromov-Witten invariants. This gives a vast generalization of the theory of relative Gromov-Witten invariants introduced by Li-Ruan, Ionel-Parker, and Jun Li, and completes a program first proposed by the second named author in 2002. One considers target spaces X carrying a log structure. Domains of stable log curves are log smooth curves. Algebraicity of the stack of such stable log maps is proven, subject only to the hypothesis that the log structure on X is fine, saturated, and Zariski. A notion of basic stable log map is introduced; all stable log maps are pull-backs of basic stable log maps via base-change. With certain additional hypotheses, the stack of basic stable log maps is proven to be proper. Under these hypotheses and the additional hypothesis that X is log smooth, one obtains a theory of log Gromov-Witten invariants.Comment: 58 pages, 5 figure

Learning-by-Doing and Cannibalization Effects at Multi-Vintage Firms: Evidence from the Semiconductor Industry

Previous studies on the measurement of learning-by-doing emphasize the importance of accounting for multi-vintage effects having an impact on firms’ production costs through economies of scope. This study shows that accounting for cannibalization effects on the demand side is equally important for the adequate measurement of learning. Since multi-vintage firms anticipate the demand-side cannibalization effects in their production optimization, a previously omitted incentive to decrease production is captured having an impact on the measurement of learning by doing. We derive an empirical model from a dynamic oligopoly game of learning-by-doing and allow cannibalization effects to enter from the demand side. Using quarterly firm-level data for the dynamic random access memory semiconductor industry, we find support for cannibalization effects entering firms’ pricing relations resulting in higher estimated learning effects.Dynamic Random Access Memory; Dynamics; Economies of Scale; Learning by Doing; Multiproduct Firms; Product Life Cycle; Semiconductors