Related papers: Modeling General Asymptotic Calabi-Yau Periods
We study periods in an integral basis near all possible singularities in one-dimensional complex structure moduli spaces of Calabi-Yau threefolds. Near large complex structure points these asymptotic periods are well understood in terms of…
In this thesis we have studied various applications of asymptotic Hodge theory in string compactifications. This mathematical framework captures how physical couplings of the resulting effective theories behave near field space boundaries…
We initiate the systematic study of flux scalar potentials and their vacua by using asymptotic Hodge theory. To begin with, we consider F-theory compactifications on Calabi-Yau fourfolds with four-form flux. We argue that a classifications…
We study the structure of string theory flux compactification for a general family of elliptic CY 3-folds. We investigate the locus of the attractor points of the flux compactification in type IIB string theory on the boundary components of…
We prove that the deformation theory of compactifiable asymptotically cylindrical Calabi-Yau manifolds is unobstructed. This relies on a detailed study of the Dolbeault-Hodge theory and its description in terms of the cohomology of the…
We present a novel strategy to systematically study complex-structure moduli stabilization in Type IIB and F-theory flux compactifications. In particular, we determine vacua in any asymptotic regime of the complex-structure moduli space by…
The tadpole conjecture suggests that the complete stabilization of complex structure deformations in Type IIB and F-theory flux compactifications is severely obstructed by the tadpole bound on the fluxes. More precisely, it states that the…
The period geometry of Calabi-Yau $n$-folds, characterised by their variations of Hodge structure governed by Griffiths transversality, a graded Frobenius algebra, an integral monodromy and an intriguing arithmetic structure, is analysed…
Generalized Calabi-Yau structures, a notion recently introduced by Hitchin, are studied in the case of K3 surfaces. We show how they are related to the classical theory of K3 surfaces and to moduli spaces of certain SCFT as studied by…
We examine instances of modularity of (rigid) Calabi-Yau manifolds whose periods are expressed in terms of hypergeometric functions. The $p$-th coefficients $a(p)$ of the corresponding modular form can be often read off, at least…
Assuming suitable convergence properties for the Gromov-Witten potential of a Calabi-Yau manifold $X$ one may construct a polarized variation of Hodge structure over the complexified K\"ahler cone of $X$. In this paper we show that, in the…
The predictions of the Mirror Symmetry are extended in dimensions n>3 and are proven for projective complete intersections Calabi-Yau varieties. Precisely, we prove that the total collection of rational Gromov-Witten invariants of such…
Motivated by the Strominger-Yau-Zaslow conjecture, we study fibre spaces whose total space has trivial canonical bundle. Especially, we are interest in Calabi-Yau varieties with fibre structure. In this paper, we only consider semi-stable…
We use a generalization of the Gibbons-Hawking ansatz to study the behavior of certain non-compact Calabi-Yau manifolds in the large complex structure limit. This analysis provides an intermediate step toward proving the metric collapse…
We develop some consequences of the connection between Calabi-Yau structures and torsion-free $G_2$ structures on compact and asymptotically cylindrical six- and seven-dimensional manifolds. Firstly, we improve the known proof that matching…
To a one-parameter family of Calabi-Yau threefolds, we can associate the extended period map by the log Hodge theory of Kato and Usui. In the present paper, we study the image of a maximally unipotent monodromy point under the extended…
We derive global constraints on the non-BPS sector of supersymmetric 2d sigma-models whose target space is a Calabi-Yau manifold. When the total Hodge number of the Calabi-Yau threefold is sufficiently large, we show that there must be…
We study an algebraic inequality for nilpotent matrices and show some interesting geometric applications: (i) obtaining topological information for nilpotent polystable Higgs bundles over a compact Riemann surface; (ii) obtaining a sharp…
The asymptotic structure of AdS spacetimes in the context of General Relativity coupled to the Maxwell field in three spacetime dimensions is analyzed. Although the fall-off of the fields is relaxed with respect to that of Brown and…
We discuss the Hodge theory of algebraic non-commutative spaces and analyze how this theory interacts with the Calabi-Yau condition and with mirror symmetry. We develop an abstract theory of non-commutative Hodge structures, investigate…