On square-zero elements in the IIB supersymmetry algebra

We describe the variety of square-zero elements in the (2,0) super Poincar\'e algebra in ten dimensions, together with its orbit stratification induced by the action of the spin group and R-symmetry. This provides a classification of all possible twisting supercharges of type IIB supergravity in a flat background. Compared to other varieties of square-zero elements in super Poincar\'e algebras, we find that the orbit structure is more involved and exhibits several novel features. Among other things, we show that there are two distinct orbits of holomorphic twisting supercharges and a number of mixed topological-holomorphic twists.