The log product formula

Algebra & Number Theory, vol. 17, pp. 1281–1323

Abstract

Let V, W be a pair of smooth varieties.We want to compare curve counts on V × W with those on V and W .The product formula in Gromov-Witten theory compares the virtual fundamental classes of stable maps to a product M g,n (V × W ) to the product of stable maps M g,n (V ) × M g,n (W ).We prove the analogous theorem for log stable maps to log smooth varieties V, W .This extends results of Y.P. Lee and F. Qu, who introduced this formula after K. Behrend.We introduce "log normal cones" and "log virtual fundamental classes," as well as modified versions of standard intersection-theoretic machinery adapted to log geometry.

Authors 1

1. Leo Herr corresponding Aachen

   Leiden University

   Affiliation as printed

   Universiteit Leiden, Netherlands