Maximal Cohen–Macaulay modules over certain Segre products

On the arithmetic rank of certain Segre products

We compute the arithmetic ranks of the defining ideals of homogeneous coordinate rings of certain Segre products arising from elliptic curves. The cohomological dimension of these ideals varies with the characteristic of the field, though the arithmetic rank does not. We also study the related set-theoretic Cohen-Macaulay property for these ideals. In [12] Lyubeznik writes: Part of what makes t...

Schur Modules and Segre Varieties

This paper is an elementary introduction to the methods of Landsberg and Manivel, [3] for finding the ideals of secant varieties to Segre varieties. We cover only the most basic topics from [3], but hope that since this is a topic which is rarely made explicit, these notes will be of some use. We assume the reader is familiar with the basic operations of multilinear algebra: tensor, symmetric, ...

Maximal Cohen-macaulay Modules over Hypersurface Rings

This paper is a brief survey on various methods to classify maximal Cohen-Macaulay modules over hypersurface rings. The survey focuses on the contributions in this topic of Dorin Popescu together with his collaborators.

Fredholm Modules over Certain Group C*-algebras

Motivated by the search for new examples of “noncommutative manifolds”, we study the noncommutative geometry of the group C*-algebras of various discrete groups. The examples we consider are the infinite dihedral group Z×σZ2 and the semidirect product group Z×σZ. We present a unified treatment of the K-homology and cyclic cohomology of these algebras.

Rank One Maximal Cohen-macaulay Modules Over