Analytic Spread of Binomial Edge Ideals

To an ideal J in a polynomial ring R over a field K we associate its analytic spread \ell(J), which is the dimension of the fiber cone F(J) of J. When J is graded and generated in a single degree d, then F(J) is a finite type K-algebra.
To a graph G we associate its binomial edge ideal:
J_G:= (x_i y_j – x_jy_i | {i,j} is an edge of G).
In this talk we will discuss recent work where sharp bounds are given for \ell(J_G) and we compute the exact value when G is a pseudoforest. We accomplish this by computing the transcendence degree trdeg_{K} F(J), of the fiber cone over K.