Seminormal graded rings and weakly normal projective varieties

Seminormal Rings (following

The Traverso-Swan theorem says that a reduced ring A is seminormal if and only if the natural homomorphism PicA→ PicA[X] is an isomorphism ([18, 17]). We give here all the details needed to understand the elementary constructive proof for this result given by Thierry Coquand in [2]. This example is typical of a new constructive method. The final proof is simpler than the initial classical one. ...

Normal Ideals of Graded Rings

For a graded domain R = k[X0, ...,Xm]/J over an arbitrary domain k, it is shown that the ideal generated by elements of degree ≥ mA, where A is the least common multiple of the weights of the Xi, is a normal ideal.

Graded Rings and Equivariant Sheaves on Toric Varieties

In this note we derive a formalism for describing equivariant sheaves over toric varieties. This formalism is a generalization of a correspondence due to Klyachko, which states that equivariant vector bundles on toric varieties are equivalent to certain sets of filtrations of vector spaces. We systematically construct the theory from the point of view of graded ring theory and this way we consi...

On Associated Graded Rings of Normal Ideals

Algebraic Cocycles on Normal, Quasi-Projective Varieties

Blaine Lawson and the author introduced algebraic cocycles on complex algebraic varieties in [FL-1] and established a duality theorem relating spaces of algebraic cocycles and spaces of algebraic cycles in [FL-2]. This theorem has non-trivial (and perhaps surprising) applications in several contexts. In particular, duality enables computations of “algebraic mapping spaces” consisting of algebra...