相关论文: On a Lefschetz-type phenomenon for elliptic Calabi…
In recent work, we conjectured that Calabi-Yau threefolds defined over $\mathbb{Q}$ and admitting a supersymmetric flux compactification are modular, and associated to (the Tate twists of) weight-two cuspidal Hecke eigenforms. In this work,…
We discuss some aspects of F-theory in four dimensions on elliptically fibered Calabi-Yau fourfolds which are Calabi-Yau threefold fibrations. A particularly simple class of such manifolds emerges for fourfolds in which the generic…
We briefly review attempts to construct string theories that yield the standard model, concentrating on models with a geometric interpretation. Calabi-Yau compactifications are discussed in the context of both the weakly coupled heterotic…
We give a complete list of a class of three-generation models in E8 x E8 heterotic string theory and its dual F-theory on an elliptic Calabi-Yau over a (generalized) Hirzebruch variety in which the divisors of the relevant line bundles…
In this paper, we study the analogue of the Shafarevich conjecture for polarized Calabi-Yau varieties. We use variations of Hodge structures and Higgs bundles to establish a criterion for the {\it rigidity} of families. We then apply the…
We recently formulated a number of Crepant Resolution Conjectures (CRC) for open Gromov-Witten invariants of Aganagic-Vafa Lagrangian branes and verified them for the family of threefold type A-singularities. In this paper we enlarge the…
We study elliptic fibrations that geometrically engineer an SU(2)$\times$ G$_2$ gauge theory realized by Weierstrass model for the collision III+$\text{I}_0^{*\text{ns}}$. We construct the four possible crepant resolutions of such a…
We introduce a new notion of deformation of complex structure, which we use as an adaptation of Kodaira's theory of deformations, but that is better suited to the study of noncompact manifolds. We present several families of deformations…
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…
Elliptic Calabi-Yau fibrations with Mordell-Weil group of rank two are constructed. Such geometries are the basis for F-theory compactifications with two abelian gauge groups in addition to non-abelian gauge symmetry. We present the…
The aim of this paper is to construct Calabi-Yau 4-folds as crepant resolutions of the quotients of a hyperk\"ahler 4-fold $X$ by a non symplectic involution $\alpha$. We first compute the Hodge numbers of a Calabi-Yau constructed in this…
We prove that there are finitely many families, up to isomorphism in codimension one, of elliptic Calabi-Yau manifolds $Y\rightarrow X$ with a rational section, provided that $\dim(Y)\leq 5$ and $Y$ is not of product-type. As a consequence,…
We study the phenomenology of the strong-coupling limit of $E_8\times E_8$ heterotic string obtained from M-theory, using a Calabi-Yau compactification. After summarizing the standard embedding results, we concentrate on non-standard…
For orbifolds admitting a crepant resolution and satisfying a hard Lefschetz condition, we formulate a conjectural equivalence between the Gromov-Witten theories of the orbifold and the resolution. We prove the conjecture for the…
We study crepant resolutions of Weierstrass models of $\text{SU}(2)\!\times\!\text{SU}(3)$-models, whose gauge group describes the non-abelian sector of the Standard Model. The $\text{SU}(2)\!\times\!\text{SU}(3)$-models are elliptic…
We systematically analyze a broad class of dual heterotic and F-theory models that give four-dimensional supergravity theories, and compare the geometric constraints on the two sides of the duality. Specifically, we give a complete…
We present a systematic way of generating F-theory models dual to nonperturbative vacua (i.e., vacua with extra tensor multiplets) of heterotic E8xE8 strings compactified on K3, using hypersurfaces in toric varieties. In all cases, the…
Applying the Ashok-Denef-Douglas estimation method to elliptic Calabi-Yau fourfolds suggests that a single elliptic fourfold ${\cal M}_{\rm max}$ gives rise to ${\cal O} (10^{272,000})$ F-theory flux vacua, and that the sum total of the…
We formulate a Crepant Resolution Correspondence for open Gromov-Witten invariants (OCRC) of toric Lagrangian branes inside Calabi-Yau 3-orbifolds by encoding the open theories into sections of Givental's symplectic vector space. The…
The aim of this paper is to construct families of Calabi--Yau 3-folds without boundary points with maximal unipotent monodromy and to describe the variation of their Hodge structures. In particular five families are constructed. In all…