Professor Ruan Yongbin has online published a research paper by Inventiones mathematicae

The logarithmic gauged linear sigma model

Inventiones mathematicae volume 225, pages1077–1154 (2021) by Qile Chen, Felix Janda & Yongbin Ruan



We introduce the notion of log R-maps, and develop a proper moduli stack of stable log R-maps in the case of a hybrid gauged linear sigma model. Two virtual cycles (canonical and reduced) are constructed for these moduli stacks. The main results are two comparison theorems relating the reduced virtual cycle to the cosection localized virtual cycle, as well as the reduced virtual cycle to the canonical virtual cycle. This sets the foundation of a new technique for computing higher genus Gromov–Witten invariants of complete intersections.

Published: 06 April 2021