Forschungsseminar: Komplexe Geometrie

13.01.2011 David Favero (UPenn/TU Wien)

Variation of GIT for toric LG-models

Abstract: Via a well-known construction of Cox, semi-projective toric varieties can be described as GIT quotients of the spectrum of the Cox ring. Choosing a degree zero element of the Cox ring, gives a function on all GIT quotients, hence each quotient can by thought of as a toric Landau-Ginzburg model. In the Calabi-Yau case, physicists Herbst, Hori, and Page, have related these LG-models as different phases of the same gauged linear sigma model, predicting equivalent categories of matrix factorizations. These predictions were proven mathematically in work of Herbst and Walcher. The general (non Calabi-Yau) case is part of joint work with M. Ballard and L. Katzarkov. Here, one obtains semi-orthogonal decompositions relating the varying GIT quotients. Combined with categorical renormalization group flow, as in the thesis of Isik, this recovers a well known result of Orlov.