Cox Rings

Coxringsaresignificantglobalinvariantsofalgebraicvarieties,naturallygeneralizinghomogeneouscoordinateringsofprojectivespaces.Thisbookprovidesalargelyself-containedintroductiontoCoxrings,withaparticularfocusonconcreteaspectsofthetheory.Besidestherigorouspresentationofthebasicconcepts,othercentraltopicsincludethecaseoffinitelygeneratedCoxringsanditsrelationtotoricgeometry;variousclassesofvarietieswithgroupactions;thesurfacecase;andapplicationsinarithmeticproblems,inparticularManin'sconjecture.Theintroductorychaptersrequireonlybasicknowledgeinalgebraicgeometry.Themoreadvancedchaptersalsotouchonalgebraicgroups,surfacetheory,andarithmeticgeometry.Eachchapterendswithexercisesandproblems.Thesecomprisemini-tutorialsandexamplescomplementingthetext,guidedexercisesfortopicsnotdiscussedinthetext,and,finally,severalopenproblemsofvaryingdifficulty.