A small resolution for triple covers in algebraic geometry

Given a triple cover p: X --> Y of varieties, we produce a new variety Z and a birational morphism f: Z --> X which is an isomorphism away from the fat-point ramification locus of p. The variety Z has a natural interpretation in terms of the data describing the triple cover, and the morphism f has an elegant geometric description.Comment: 9 page

Surfaces of minimal degree of tame representation type and mutations of Cohen-Macaulay modules

We provide two examples of smooth projective surfaces of tame CM type, by showing that any parameter space of isomorphism classes of indecomposable ACM bundles with fixed rank and determinant on a rational quartic scroll in projective 5-space is either a single point or a projective line. For surfaces of minimal degree and wild CM type, we classify rigid Ulrich bundles as Fibonacci extensions. For the rational normal scrolls S(2,3) and S(3,3), a complete classification of rigid ACM bundles is given in terms of the action of the braid group in three strands.Comment: This version is meant to amend two inaccurate statements appearing in the published pape

The Cohen-Macaulay representation type of arithmetically Cohen-Macaulay varieties

We show that all reduced closed subschemes of projective space that have a Cohen-Macaulay graded coordinate ring are of wild Cohen-Macaulay type, except for a few cases which we completely classify.Comment: Completely new version. The main result now covers reducible subschemes and cones. Many proofs have been simplified and correcte