We define enumerative invariants associated to a hybrid Gauged Linear Sigma Model. We prove that in the relevant special cases these invariants recover both the Gromov-Witten type invariants defined by Chang-Li and Fan-Jarvis-Ruan using cosection localization as well as the FJRW type invariants constructed by Polishchuk-Vaintrob. The invariants are defined by constructing a "fundamental factorization" supported on the moduli space of Landau-Ginzburg maps to a convex hybrid model. This gives the kernel of a Fourier-Mukai transform; the associated map on Hochschild homology defines our theory.
Ionut Ciocan-Fontanine, University of Minnesota, Minneapolis, Minnesota, and Korea Institute for Advanced Study, Seoul, Republic of Korea.
David Favero, University of Minnesota, Minneapolis, Minnesota, and Korea Institute for Advanced Study, Seoul, Republic of Korea.
Jeremy Guere, Universite Grenoble Alpes, France.
Bumsig Kim, Korea Institute for Advanced Study, Seoul, Republic of Korea.
Mark Shoemaker, Colorado State University, Fort Collins, Colorado.
