Mixed toric residues and Calabi-Yau complete intersections

Details Mixed toric residues and Calabi-Yau complete intersections Mixed toric residues and Calabi-Yau complete intersections

2002-06-06

arxiv.org/abs/math/0206057v2

Mathematics

Algebraic Geometry

AMS LaTeX; 28 pages, 1 figure

Scientific paper

Using 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.

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