Point modules of quantum projective spaces

In this note we give an explicit description of the irreducible components of the reduced point varieties of quantum polynomial algebras.Comment: 4 pages, a short not

Formal structures and representation spaces

M. Kapranov introduced and studied in math.AG/9802041 the noncommutative formal structure of a smooth affine variety. In this note we show that his construction is a special case of microlocalization and extend it in a functorial way to representation schemes of affine algebras. We describe the formal completion in the case of path algebras of quivers and initiate the study of their finite dimensional representations

The point variety of quantum polynomial rings

We show that the reduced point variety of a quantum polynomial algebra is the union of specific linear subspaces in $\mathbb{P}^n$, we describe its irreducible components and give a combinatorial description of the possible configurations in small dimensions.Comment: 10 pages, an extended version of arxiv.org/abs/1506.0651