1994/12/18 by Victor V. Batyrev, Batyrev, Victor V., Lev Borisov +1 · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.alg-geom/9412017
openalex publication_date 1994/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate Hodge-theoretic properties of Calabi-Yau complete intersections V of r semi-ample divisors in d-dimensional toric Fano varieties having at most Gorenstein singularities. Our main purpose is to show that the combinatorial duality proposed by second author agrees with the duality for Hodge numbers predicted by mirror symmetry. It is expected that the complete verification of mirror symmetry predictions for singular Calabi-Yau varieties V of arbitrary dimension demands considerations of so called \em string-theoretic Hodge numbers hp,q\rm st(V). We restrict ourselves to the string-theoretic Hodge numbers h0,q\rm st(V) and h1,q\rm st(V) (0 ≤ q ≤ d-r) which coincide with the usual Hodge numbers h0,q(\widehatV) and h1,q(\widehatV) of a MPCP-desingularization \widehatV of V.