Ruoxi Li
University of Illinois Urbana-Champaign (UIUC)
Title
Shifted Logarithmic Functions and more
Abstract
To some extent, a perfect obstruction theory in the sense of Behrend--Fantechi is the shadow of a quasi-smooth derived Deligne--Mumford stack, while a cosection of a perfect obstruction theory in the sense of Kiem--Li is the shadow of a (-1)-shifted function on a quasi-smooth derived Deligne--Mumford stack. In this talk, we will introduce shifted logarithmic functions on derived stacks equipped with log structures of Deligne--Faltings type, and logarithmic cosections of perfect obstruction theories. As an application, we will present a decomposition theorem for virtual cycles, after Log GLSM. If time permits, we will discuss another facet of shifted logarithmic functions: their derived critical loci carry shifted logarithmic symplectic structures, building on the work of Calaque-Safronov.
