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...Comptesrendus mathematique vivekshende toricmirrorsymmetryrevisited volume p thisarticleislicensedunderthe creativecommonsattribution internationallicense http creativecommons org licenses by les comptes rendus sont membres du centre mersenne pour l edition scientique ouverte www vol https doi crmath algebraicgeometry mathematicalphysics geometriealgebrique physique a b centerforquantummathematics universityofsoutherndenmark campusvej odense denmark departmentofmathematics ucberkeley berkeleyca usa e mail vivek vijay shende gmail com abstract the cox construction presents toric variety as quotient of ane space torus category ofcoherentsheavesonthecorrespondingstackthushasanevidentdescriptionasinvariantsinaquotientof thecategoryofmodulesoverapolynomialring herewegivethemirrortothisdescription andinparticular acleannewproofofmirrorsymmetryforsmoothtoricstacks funding my work is partially supported villum fonden investigator danish national research foundation dnrf novo nordisk nnfoc and ...