This paper studies geometric properties of the Iterated Matrix Multiplication polynomial and the hypersurface that it defines. We focus on geometric aspects that may be relevant for complexity theory such as the symmetry group of the polynomial, the dual variety and the Jacobian loci of the hypersurface, that are computed with the aid of representation theory of quivers.

We give an upper bound for the minimal discrepancies of hypersurface singularities. As an application, we show that Shokurov’s conjecture is true for log-terminal threefolds.

Let (9,+1 be the ring of germs of holomorphic functions (C ~+ 1, 0 ) ~ C. There are many important equivalence relations that have been defined on the elements of (9+ 1. ~ ' , ~s and ~f-equivalence are well known in function theory. Each of these equivalence relations can be defined in terms of a Lie group action on (9 +1For instance two functions are defined to be ~-equivalent if they are the ...

We present results on multiplicity theory. Differential operators on smooth schemes play a central role in the study of the multiplicity of an embedded hypersurface at a point. This follows from the fact that the multiplicity is defined by the Taylor development of the defining equation at such point. On the other hand, the multiplicity of a hypersurface at a point can be expressed in terms of ...