Mixed Toric Residues and Calabi-Yau Complete Intersections

Аннотация

Using the Caley trick, we define the notions of mixed toric residues and mixed Hessians associated with $f_1, \ldots, f_r$ Laurent polynomials. We conjecture that the values of the mixed toric residues on the mixed Hessians are determined by mixwd volumes of the Newton polypopes of $f_1, \ldots, f_r$. 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.