2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64238Using Cayley trick, we define the notions of mixed toric residues and mixed Hessians associated with $r$ Laurent polynomials $f_1,...,f_r$.We conjecture that the values of mixed toric residues on the mixed Hessians are determined by mixed volumes of the Newton polytopes of $f_1,...,f_r$. Using mixed toric residues, we generalize our Toric Residue Mirror Conjecture to the case of Calabi-Yau complete intersections in Gorenstein toric Fano varieties obtained from nef-partitions of reflexive polytopes.AMS LaTeX; 28 pages, 1 figureAlgebraic GeometryHigh Energy Physics - Theory14M25text