Related papers: Efficient Algorithm for Generating Homotopy Inequi…
Fine, regular, and star triangulations (FRSTs) of four-dimensional reflexive polytopes give rise to toric varieties, within which generic anticanonical hypersurfaces yield smooth Calabi-Yau threefolds. We introduce CYTransformer, a deep…
We study Calabi-Yau threefolds with large Hodge numbers by constructing and counting triangulations of reflexive polytopes. By counting points in the associated secondary polytopes, we show that the number of fine, regular, star…
We study the birational geometry (i.e., K\"ahler moduli space) of Calabi--Yau (CY) threefold hypersurfaces in toric varieties arising from four-dimensional reflexive polytopes. In particular, it has been observed that the birational classes…
We implement Genetic Algorithms for triangulations of four-dimensional reflexive polytopes which induce Calabi-Yau threefold hypersurfaces via Batyrev's construction. We demonstrate that such algorithms efficiently optimize physical…
We provide the first estimate of the number of fine, regular, star triangulations of the four-dimensional reflexive polytopes, as classified by Kreuzer and Skarke (KS). This provides an upper bound on the number of Calabi-Yau threefold…
We explain how to form a novel dataset of simply connected Calabi-Yau threefolds via the Gross-Siebert algorithm. We expect these to degenerate to Calabi-Yau toric hypersurfaces with certain Gorenstein (not necessarily isolated)…
We enumerate topologically-inequivalent compact Calabi-Yau threefold hypersurfaces. By computing arithmetic and algebraic invariants and the Gopakumar-Vafa invariants of curves, we prove that the number of distinct simply connected…
Batyrev's construction provides a map from fine, regular, star triangulations (FRSTs) of 4D reflexive polytopes to smooth Calabi-Yau threefolds (CYs). We prove that there are at most $10^{296}$ diffeomorphism classes of CYs produced in this…
We analyze freely-acting discrete symmetries of Calabi-Yau three-folds defined as hypersurfaces in ambient toric four-folds. An algorithm which allows the systematic classification of such symmetries which are linearly realised on the toric…
Kreuzer and Skarke famously produced the largest known database of Calabi-Yau threefolds by providing a complete construction of all 473,800,776 reflexive polyhedra that exist in four dimensions. These polyhedra describe the singular limits…
Calabi-Yau manifolds can be obtained as hypersurfaces in toric varieties built from reflexive polytopes. We generate reflexive polytopes in various dimensions using a genetic algorithm. As a proof of principle, we demonstrate that our…
The classification of 4D reflexive polytopes by Kreuzer and Skarke allows for a systematic construction of Calabi-Yau hypersurfaces as fine, regular, star triangulations (FRSTs). Until now, the vastness of this geometric landscape remains…
Calabi-Yau four-folds may be constructed as hypersurfaces in weighted projective spaces of complex dimension 5 defined via weight systems of 6 weights. In this work, neural networks were implemented to learn the Calabi-Yau Hodge numbers…
We compare the sets of Calabi-Yau threefolds with large Hodge numbers that are constructed using toric hypersurface methods with those can be constructed as elliptic fibrations using Weierstrass model techniques motivated by F-theory. There…
Using a fully connected feedforward neural network we study topological invariants of a class of Calabi--Yau manifolds constructed as hypersurfaces in toric varieties associated with reflexive polytopes from the Kreuzer--Skarke database. In…
Using the Kreuzer-Skarke database of 4-dimensional reflexive polytopes, we systematically constructed a new database of orientifold Calabi-Yau threefolds with $h^{1,1}(X) \leq 12$. Our approach involved non-trivial $\mathbb{Z}_2$…
The diffeomorphism class of simply-connected smooth Calabi-Yau threefolds with torsion-free cohomology is determined via certain basic topological invariants: the Hodge numbers, the triple intersection form, and the second Chern class. In…
We compute the integral homology (including torsion), the topological K-theory, and the Hodge structure on cohomology of Calabi-Yau threefold hypersurfaces and complete intersections in Gorenstein toric Fano varieties. The methods are…
We present a classification algorithm for Calabi-Yau complete intersections arising from nef-partitions in fake weighted projective spaces, allowing us to determine all such complete intersections up to dimension five. Furthermore, we…
We describe an efficient, construction independent, algorithmic test to determine whether Calabi--Yau threefolds admit a structure compatible with the Large Volume moduli stabilization scenario of type IIB superstring theory. Using the…