Motivated by Hassett's weighted pointed stable curves, we use the log minimal model program to construct compact moduli spaces parameterizing weighted stable elliptic surfaces — elliptic fibrations with section and marked fibers each weighted between zero and one. Moreover, we show that the domain of weights admits a wall and chamber structure, describe the induced wall-crossing morphisms on the moduli spaces as the weight vector varies, and describe the surfaces that appear on the boundary of the moduli space. The main technical result is a proof of invariance of log plurigenera for slc elliptic surface pairs with arbitrary weights.
All Science Journal Classification (ASJC) codes
- 14J10 (primary)
- 14J27 (secondary)