On the stringy Hodge numbers of mirrors of quasi-smooth Calabi-Yau hypersurfaces

Abstract

Mirrors X ∨ of quasi-smooth Calabi-Yau hypersurfaces X in weighted projective spaces P(w 0 , . . . , w d ) can be obtained as Calabi-Yau compactifications of non-degenerate affine toric hypersurfaces defined by Laurent polynomials whose Newton polytope is the lattice simplex spanned by d + 1 lattice vectors v i satisfying the relation i w i v i = 0. In this paper, we compute the stringy E-function of mirrors X ∨ and compare it with the Vafa's orbifold E-function of quasi-smooth Calabi-Yau hypersurfaces X. As a result, we prove the equalities of Hodge numbers h p,q str (X ∨ ) = h d−1−p,q orb (X) for all p, q and d as it is expected in mirror symmetry.

Machine Learning Algebraic Geometry for Physics

“…such that normalised weights q i = w i / i (w i ) are operated on with multiple divisibility checks and other complicated computation steps involving age(l) = 4 i=0 θi (l) and size(l) = age(l)+age( i (w i )−l); where in (R/Z) 5 , θi (l) is the canonical representative of lq i [45,46].…”