Related papers: Calabi-Yau complete intersections in fake weighted…
Most of Calabi-Yau manifolds that have been considered by physicists are complete intersection Calabi-Yau manifolds of toric varieties or some quotients of product types. Purpose of this paper is to introduce a different and rather new kind…
We investigate the open mirror symmetry of certain non-complete intersection Calabi- Yau 3-folds, so called pfaffian Calabi-Yau. We perform the prediction of the number of disk invariants of several examples by using the direct integration…
We describe the possible noncommutative deformations of complex projective three-space by exhibiting the Calabi--Yau algebras that serve as their homogeneous coordinate rings. We prove that the space parametrizing such deformations has…
We prove a formula for the Hodge numbers of square-free divisors of Calabi-Yau threefold hypersurfaces in toric varieties. Euclidean branes wrapping divisors affect the vacuum structure of Calabi-Yau compactifications of type IIB string…
We review the construction of families of projective varieties, in particular Calabi--Yau threefolds, as quasilinear sections in weighted flag varieties. We also describe a construction of tautological orbi-bundles on these varieties, which…
We show that "non-polynomial" deformations of semiample (minimal) nondegenerate Calabi-Yau hypersurfaces in complete simplicial toric varieties can be realized as quasismooth complete intersections in higher dimensional simplicial toric…
We present an algorithm for efficiently exploring inequivalent Calabi-Yau threefold hypersurfaces in toric varieties. A direct enumeration of fine, regular, star triangulations (FRSTs) of polytopes in the Kreuzer-Skarke database is…
We give a Hodge-theoretic criterion for a Calabi--Yau variety to have finite Weil--Petersson distance on higher dimensional bases up to a set of codimension $\geq 2$. The main tool is variation of Hodge structures and variation of mixed…
We study an example of complete intersection Calabi-Yau threefold due to Libgober and Teitelbaum arXiv:alg-geom/9301001, and verify mirror symmetry at a cohomological level. Direct computations allow us to propose an analogue to the…
At special loci in their moduli spaces, Calabi-Yau manifolds are endowed with discrete symmetries. Over the years, such spaces have been intensely studied and have found a variety of important applications. As string compactifications they…
Maschke's Calabi-Yau threefold is the double cover of projective three space branched along Maschke's octic surface. This surface is defined by the lowest degree invariant of a certain finite group acting on a four dimensional vector space.…
Global F-theory compactifications whose fibers are realized as complete intersections form a richer set of models than just hypersurfaces. The detailed study of the physics associated with such geometries depends crucially on being able to…
We undertake a systematic scan of vector bundles over spaces from the largest database of known Calabi-Yau three-folds, in the context of heterotic string compactification. Specifically, we construct positive rank five monad bundles over…
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…
We state several questions, and prove some partial results, about the Chow ring $A^\ast(X)$ of complete intersections in projective space. For one thing, we prove that if $X$ is a general Calabi-Yau hypersurface, the intersection product…
In Calabi-Yau fourfold compactifications of M-theory with flux, we investigate the possibility of partial supersymmetry breaking in the three-dimensional effective theory. To this end, we place the effective theory in the framework of…
Let Y be a Calabi-Yau complete intersection in a weighted projective space. We show that the space of quadratic invariants of the hypergeometric group associated with the twisted I-function is one-dimensional, and spanned by the Gram matrix…
We show that non-trivial SU(3) structures can be constructed on large classes of Calabi-Yau three-folds. Specifically, we focus on Calabi-Yau three-folds constructed as complete intersections in products of projective spaces, although we…
Recent results on duality between string theories and connectedness of their moduli spaces seem to go a long way toward establishing the uniqueness of an underlying theory. For the large class of Calabi-Yau 3-folds that can be embedded as…
A nef-partition for a weighted complete intersection is a combinatorial structure on its weights and degrees which is important for Mirror Symmetry. It is known that nef-partitions exist for smooth well-formed Fano weighted complete…