Search results for "Calabi-Yau"
showing 9 items of 9 documents
New fourfolds from F-theory
2015
In this paper, we apply Borcea-Voisin's construction and give new examples of fourfolds containing a del Pezzo surface of degree six, which admit an elliptic fibration on a smooth threefold. Some of these fourfolds are Calabi-Yau varieties, which are relevant for the $N=1$ compactification of Type IIB string theory known as $F$-Theory. As a by-product, we provide a new example of a Calabi--Yau threefold with Hodge numbers $h^{1,1}=h^{2,1}=10$.
Groups acting freely on Calabi-Yau threefolds embedded in a product of del Pezzo surfaces
2011
In this paper, we investigate quotients of Calabi-Yau manifolds $Y$ embedded in Fano varieties $X$, which are products of two del Pezzo surfaces — with respect to groups $G$ that act freely on $Y$. In particular, we revisit some known examples and we obtain some new Calabi-Yau varieties with small Hodge numbers. The groups $G$ are subgroups of the automorphism groups of $X$, which is described in terms of the automorphism group of the two del Pezzo surfaces.
New examples of Calabi-Yau threefolds and genus zero surfaces
2012
We classify the subgroups of the automorphism group of the product of 4 projective lines admitting an invariant anticanonical smooth divisor on which the action is free. As a first application, we describe new examples of Calabi-Yau 3-folds with small Hodge numbers. In particular, the Picard number is 1 and the number of moduli is 5. Furthermore, the fundamental group is non-trivial. We also construct a new family of minimal surfaces of general type with geometric genus zero, K^2=3 and fundamental group of order 16. We show that this family dominates an irreducible component of dimension 4 of the moduli space of the surfaces of general type.
Diffeomorphism classes of Calabi-Yau varieties
2016
In this article we investigate diffeomorphism classes of Calabi-Yau threefolds. In particular, we focus on those embedded in toric Fano manifolds. Along the way, we give various examples and conclude with a curious remark regarding mirror symmetry.
Some Remarks on Calabi-Yau Manifolds
2010
Here we focus on the geometry of the “mirror quintic” Y and its generalizations. In particular, we illustrate how to obtain new birational models of Y . The article under review can be regarded as an announcement of or supplement to results in forthcoming papers of the author and his collaborators concerning quintic threefolds, the Dwork pencil, and its natural generalization to higher dimensions [G. Bini, “Quotients of hypersurfaces in weighted projective space”, preprint, arxiv.org/ abs/0905.2099, Adv. Geom., to appear; G. Bini, B. van Geemen and T. L. Kelly, “Mirror quintics, discrete symmetries and Shioda maps”, preprint, arxiv.org/abs/0809. 1791, J. Algebraic Geom., to appear; G. Bini …
A closer look at mirrors and quotients of Calabi-Yau threefolds
2016
Let X be the toric variety (P1)4 associated with its four-dimensional polytope 1. Denote by X˜ the resolution of the singular Fano variety Xo associated with the dual polytope 1o. Generically, anticanonical sections Y of X and anticanonical sections Y˜ of X˜ are mirror partners in the sense of Batyrev. Our main result is the following: the Hodge-theoretic mirror of the quotient Z associated to a maximal admissible pair (Y, G) in X is not a quotient Z˜ associated to an admissible pair in X˜ . Nevertheless, it is possible to construct a mirror orbifold for Z by means of a quotient of a suitable Y˜. Its crepant resolution is a Calabi-Yau threefold with Hodge numbers (8, 4). Instead, if we star…
Modular Calabi-Yau threefolds of level eight
2005
In the studies on the modularity conjecture for rigid Calabi-Yau threefolds several examples with the unique level 8 cusp form were constructed. According to the Tate Conjecture correspondences inducing isomorphisms on the middle cohomologies should exist between these varieties. In the paper we construct several examples of such correspondences. In the constructions elliptic fibrations play a crucial role. In fact we show that all but three examples are in some sense built upon two modular curves from the Beauville list.
Deformations of Calabi-Yau manifolds in Fano toric varieties
2020
In this article, we investigate deformations of a Calabi-Yau manifold $Z$ in a toric variety $F$, possibly not smooth. In particular, we prove that the forgetful morphism from the Hilbert functor $H^F_Z$ of infinitesimal deformations of $Z$ in $F$ to the functor of infinitesimal deformations of $Z$ is smooth. This implies the smoothness of $H^F_Z $ at the corresponding point in the Hilbert scheme. Moreover, we give some examples and include some computations on the Hodge numbers of Calabi-Yau manifolds in Fano toric varieties.
An unbounded family of log Calabi–Yau pairs
2016
We give an explicit example of log Calabi-Yau pairs that are log canonical and have a linearly decreasing Euler characteristic. This is constructed in terms of a degree two covering of a sequence of blow ups of three dimensional projective bundles over the Segre-Hirzebruch surfaces ${\mathbb F}_n$ for every positive integer $n$ big enough.