Related papers: All Complete Intersection Calabi-Yau Four-Folds
We produce counterexamples to the birational Torelli theorem for Calabi-Yau manifolds in arbitrarily high dimension: this is done by exhibiting a series of non birational pairs of Calabi-Yau $(n^2-1)$-folds which, for $n \geq 2$ even, admit…
It has recently been demonstrated that Feynman integrals relevant to a wide range of perturbative quantum field theories involve periods of Calabi-Yaus of arbitrarily large dimension. While the number of Calabi-Yau manifolds of dimension…
During the last years we have generated a large number of data related to Calabi-Yau hypersurfaces in toric varieties which can be described by reflexive polyhedra. We classified all reflexive polyhedra in three dimensions leading to K3…
We introduce some new algebraic structures arising naturally in the geometry of Calabi-Yau manifolds and mirror symmetry. We give a universal construction of Calabi-Yau algebras in terms of a noncommutative symplectic DG algebra resolution.…
We find that for many Calabi-Yau threefolds with elliptic or genus one fibrations mirror symmetry factorizes between the fiber and the base of the fibration. In the simplest examples, the generic CY elliptic fibration over any toric base…
We describe the mirror of the Z orbifold as a representation of a class of generalized Calabi-Yau manifolds that can be realized as manifolds of dimension five and seven. Despite their dimension these correspond to superconformal theories…
Calabi-Yau manifolds are important objects in algebraic geometry and in theoretical physics. A hypothesis of mirror symmetry is that Calabi-Yau manifolds of dimension 3 come in pairs, with the Hodge numbers of one manifold mirroring the…
Mirror Symmetry, Picard-Fuchs equations and instanton corrected Yukawa couplings are discussed within the framework of toric geometry. It allows to establish mirror symmetry of Calabi-Yau spaces for which the mirror manifold had been…
In this work we consider quotients of elliptically fibered Calabi-Yau threefolds by freely acting discrete groups and the associated physics of F-theory compactifications on such backgrounds. The process of quotienting a Calabi-Yau geometry…
The purpose of this note is to extend the results obtained in [arXiv:1303.6970] in two ways. First, the six-dimensional F-theory compactifications with U(1) x U(1) gauge symmetry on elliptic Calabi-Yau threefolds, constructed as a…
We present a list of Calabi-Yau threefolds known to us, and with holonomy groups that are precisely SU(3), rather than a subgroup, with small Hodge numbers, which we understand to be those manifolds with height $(h^{1,1}+h^{2,1})\le 24$.…
This work develops new ideas and tools to establish wall-crossing in Calabi-Yau four categories as originally conjectured by Gross-Joyce-Tanaka. In the process, I set up some necessary new language, including a natural refinement of Joyce's…
In this paper, we show that if $(X,g)$ is an oriented four dimensional Einstein manifold which is self-dual or anti-self-dual then superminimal surfaces in $X$ of appropriate spin enjoy the Calabi-Yau property, meaning that every immersed…
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…
Our main results are: (1) The complex a Lagrangian points of a non-complex Lagrangian $2n$-dimensional submanifold $F:M\ra N$, immersed with parallel mean curvature and with equal Kaehler angles into a Kaehler-Einstein manifold $(N,J,g)$ of…
A method for constructing explicit Calabi-Yau metrics in six dimensions in terms of an initial hyperkahler structure is presented. The equations to solve are non linear in general, but become linear when the objects describing the metric…
Finding Ricci-flat (Calabi-Yau) metrics is a long standing problem in geometry with deep implications for string theory and phenomenology. A new attack on this problem uses neural networks to engineer approximations to the Calabi-Yau metric…
In this article, we study mirror symmetry for pairs of singular Calabi--Yau manifolds which are double covers of toric manifolds. Their period integrals can be seen as certain `fractional' analogues of those of ordinary complete…
We investigate the globally generated vector bundles on complete intersection Calabi-Yau threefolds with the first Chern class at most 2. We classify all the globally generated vector bundles of an arbitrary rank on quintic in…
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…