Kurs:Vector bundles and ideal closure operations (MSRI 2012)

A bundle found in the botanical garden

Barbecue

The Californian bears are loosing versus Nevada

Strange fox (new species?) seen in the botanical garden

Oakland pride

This is a short course on vector bundles, their torsors and ideal closure operations given by Holger Brenner at the Joint Introductory Workshop: Cluster Algebras and Commutative Algebra at the MSRI in September/August 2012 (see http://www.msri.org/web/msri/scientific/workshops/all-workshops/show/-/event/Wm557). For complete notes in Pdf see here.

Lecture 1 - Linear equations, forcing algebras and ideal closure operations

Lecture 2 - Vector bundles and their torsors

Lecture 3 - Vector bundles on projective curves

Material for Tutorial Session

Lectures and Tutorial together and slightly extended

Further reading

Forcing algebras, syzygy bundles, and tight closure (Holger Brenner, survey article)

Some remarks on the affineness of ${}{\mathbb {A} }^{1}$-bundles (Holger Brenner, survey article)

A guide to closure operations in commutative algebra (Neil Epstein, survey article)

The theory of tight closure from the viewpoint of vector bundles (Holger Brenner, Habilitationsschrift)

Tight closure and plus closure in dimension two (Holger Brenner)

On the arithmetic of tight closure (Holger Brenner and Moty Katzman)

Tight closure does not commute with localization (Holger Brenner and Paul Monsky)

Continuous solutions to algebraic forcing equations (Holger Brenner)

Continuous closure, axes closure, and natural closure (Neil Epstein and Mel Hochster)

Continuous closure of sheaves (János Kollár)

John Baez explains the use of torsors in physics

Problem list