Holonomicity of GKZ-systems


Tsung-Ju Lee ( National Taiwan University )
2015-03-13  09:10 - 11:00
Room 101, Mathematics Research Center Building (ori. New Math. Bldg.)

One way to construct (projective) CY varieties is taking suitable hyperplane sections. When the ambient space is a smooth projective variety whose anti-canonical bundle is very ample, the (generic) global sections of it give CYs. If in addition that the ambient space is toric, there is a torus action on this section space. Hence the period integrals have supernumerary symmetries. One way to characterize this is to find the equations they should satisfy. This is the so-called GKZ-system, introduced by Gelfand et al.
The goal of this talk is to explain these phenomena. And show that the GKZ-system, regarded as a $D$-module, is indeed holonomic. Furthermore, I will also show the dimension of solution space is given by combinatorial data associated to the toric variety.