Hodge numbers of generalised Borcea–Voisin threefolds

Abstract

We shall reproof formulas for the Hodge numbers of Calabi-Yau threefolds of Borcea-Voisin type constructed by A. Cattaneo and A. Garbagnati, using the orbifold cohomology formula and the orbifold Euler characteristic.

Higher dimensional Calabi–Yau manifolds of Kummer type

“…There are many relations among numerical invariants of S 6 . Some of them were pointed out in [CG16] and [Bur18]. Most of them follow from adopted notation 3.4.1 and Riemann-Hurwitz formula (see [CG16]).…”

“…The authors gave a detailed crepant resolution and computed the Hodge numbers of the resulting algebraic varieties. For all possible orders they computed the Hodge numbers of these varieties and constructed elliptic fibrations on them, in [Bur18] we gave much simpler derivations of formulas for Hodge numbers using Chen-Ruan cohomology 3.1. 2.2.…”

“…Most of them follow from adopted notation 3.4.1 and Riemann-Hurwitz formula (see [CG16]). In [Bur18] we got new relation by comparing Stringy Euler Characteristic of Y 6,2 with the Euler characteristic computed from orbifold Hodge numbers.…”

“…In the present section we shall use the same idea as in [Bur18], moreover we shall examine another formulas i.e. Hurwitz formula and holomorphic and topological Lefschetz numbers.…”

Zeta function of some Kummer Calabi-Yau 3-folds

“…The aim of this work is to give a formula for the Hodge numbers and zeta function of Kum 3 (E, G) using the Chen-Ruan orbifold cohomology theory ( [CR04]) and the description of the Frobenius action on the orbifold cohomology ( [Ros07]). In [Bur18], [Bur20], [Bur21] we successfully used that approach in order to compute Hodge numbers and zeta function of manifolds (X 1 × X 2 × . .…”