Cox rings

authored by

Ivan Arzhantsev, Ulrich Derenthal, Jürgen Hausen, Antonio Laface

Abstract

In this chapter we introduce the Cox ring and, more generally, the Cox sheaf and its geometric counterpart, the characteristic space. In addition, algebraic and geometric aspects are discussed. Section 1.1 is devoted to commutative algebras graded by monoids. In Section 1.2, we recall the correspondence between actions of quasitori (also called diagonalizable groups) on affine varieties and affine algebras graded by abelian groups and provide the necessary background on good quotients. Section 1.3 is a first step toward constructing Cox rings.

Organisation(s)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik
Riemann Center for Geometry and Physics

External Organisation(s)

Lomonosov Moscow State University
Eberhard Karls Universität Tübingen
Universidad de Concepcion

Type

Monografie

No. of pages

530

Publication date

2015

Publication status

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Mathematik (insg.)

Electronic version(s)

https://doi.org/10.1017/cbo9781139175852 (Access: Geschlossen)