Details
| Original language | English |
|---|---|
| Publisher | Cambridge University Press |
| Number of pages | 530 |
| ISBN (electronic) | 9781139175852 |
| ISBN (print) | 9781107024625 |
| Publication status | Published - 2015 |
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.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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Cambridge University Press, 2015. 530 p.
Research output: Book/Report › Monograph › Research › peer review
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TY - BOOK
T1 - Cox rings
AU - Arzhantsev, Ivan
AU - Derenthal, Ulrich
AU - Hausen, Jürgen
AU - Laface, Antonio
N1 - Funding information: I would liekto tanhk DrDoyle Baker, Dr Stphean Weie,sandDr Christani NolteoftehIntrneatinoal InsttituoefTropical Agricultreu(IITA), Yaounde, Cameroon, for teihr intleecltaluinput and consistntencouragementI.would also liektotanhkDrBakerandDrWeiesfor® nancialapprovalfortehprojecinctudilng costosf satllieetimgery aand ground-uttinrhg. The encouragement given by Professor Ronald Smitohf tehYale Centr efor Earth Observatoniin compltiegntishproject at Yale is grateullyfacknowledged. Reviews provided by Dr Mark Ashtn,oProfessor John Lyon, andtehtowanonymous reviewers are highly appreciatd.eDr Nolte provided invaluable support inground-uttinrhg. Mr Afene Obam James, andMr Tam Antinoe Duprony, tehtowforesty rexpertsoftehOcNeatonial de Deelvpomnt deseForet(OsADENF), Ministreede L’Environment et des Foretwsere mainly responsible foraconsistnteforest clssaic® toaniandspeciseidet® nciatoni.Ms Umeo plrovided tehediortial hel, pMr Sam Ofdoie lanalyzed sttasticail datseat, Msr John Babalolaprovided able secearrital assistnca, aendMr Godson Bright was responsible for graphis.cAll teihr assistncaisegrateullyfacknowledged. The funding for tehprojeccatmefrom a grant from tehAltrneatveito Slash-nda-uBrn project supportebdytehGlboal Environmntal eFaciltiy(GEF) of UnitdeNatonis Deelvpomnt Preogramme (UND. I aPm grat)eul ffor tishsupport.
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84952760859&partnerID=8YFLogxK
U2 - 10.1017/cbo9781139175852
DO - 10.1017/cbo9781139175852
M3 - Monograph
AN - SCOPUS:84952760859
SN - 9781107024625
BT - Cox rings
PB - Cambridge University Press
ER -