相关论文: Fibration structure in toric hypersurface Calabi-Y…

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…

In this study, we introduce a new class of rational elliptic 3-folds, which we refer to as "1/2 Calabi-Yau 3-folds". We construct elliptically fibered Calabi-Yau 3-folds by utilizing these rational elliptic 3-folds. The construction yields…

We present a complete classification of all arrangements of eight planes in projective threespace that give rise to double octic Calabi-Yau threefolds. Building on earlier work, we determine all 455 combinatorial types and describe the…

In this paper we discuss four methods of proving modularity of Calabi--Yau threefolds with $h^{12}=1$: existence of elliptic ruled surfaces inside (Hulek-Verrill), correspondence with a product of an elliptic curve and a K3 surface…

We propose a way to examine N=1 and N=2 string dualities on Calabi-Yau three-folds or extensions. Our way is to find out or to construct two types of toric representations of a Calabi-Yau three-fold, which contain phases topologically…

We construct smooth Calabi-Yau threefolds Z, torus-fibered over a dP_9 base, with fundamental group Z_2 X Z_2. To do this, the structure of rational elliptic surfaces is studied and it is shown that a restricted subset of such surfaces…

A construction of Calabi-Yaus as quotients of products of lower-dimensional spaces in the context of weighted hypersurfaces is discussed, including desingularisation. The construction leads to Calabi-Yaus which have a fiber structure, in…

We consider F-theory compactifications on genus-one fibered Calabi-Yau manifolds with their fibers realized as hypersurfaces in the toric varieties associated to the 16 reflexive 2D polyhedra. We present a base-independent analysis of the…

We study sections of a Calabi-Yau threefold fibered over a curve by K3 surfaces. We show that there exist infinitely many isolated sections on certain K3 fibered Calabi-Yau threefolds and the subgroup of the N\'eron-Severi group generated…

In this paper, we apply Borcea--Voisin's construction and give new examples of Calabi--Yau fourfolds $Y$, which admit an elliptic fibration onto a smooth threefold $V$, whose singular fibers of type $I_5$ lie above a del Pezzo surface $dP…

We present an exhaustive, constructive, classification of the Calabi-Yau four-folds which can be described as complete intersections in products of projective spaces. A comprehensive list of 921,497 configuration matrices which represent…

We carry out a systematic analysis of Calabi-Yau threefolds that are elliptically fibered with section ("EFS") and have a large Hodge number h^{2, 1}. EFS Calabi-Yau threefolds live in a single connected space, with regions of moduli space…

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…

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…

Reflexive polyhedra encode the combinatorial data for mirror pairs of Calabi-Yau hypersurfaces in toric varieties. We investigate the geometrical structures of circumscribed polytopes with a minimal number of facets and of inscribed…

The Hodge numbers of generic elliptically fibered Calabi-Yau threefolds over toric base surfaces fill out the "shield" structure previously identified by Kreuzer and Skarke. The connectivity structure of these spaces and bounds on the Hodge…

We present the last missing details of our algorithm for the classification of reflexive polyhedra in arbitrary dimensions. We also present the results of an application of this algorithm to the case of three dimensional reflexive…

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 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 investigate Calabi--Yau three folds which are small resolutions of fiber products of elliptic surfaces with section admitting reduced fibers. We start by the classification of all fibers that can appear on such varieties. Then, we find…