Related papers: Special K\"ahler Geometry. Does there Exist a Prep…
Motivated by constructions appearing in mirror symmetry, we study special representatives of complexified K\"ahler classes, which extend the notions of constant scalar curvature and extremal representatives for usual K\"ahler classes. In…
We present a formulation of the coupling of vector multiplets to N=2 supergravity which is symplectic covariant (and thus is not based on a prepotential) and uses superconformal tensor calculus. We do not start from an action, but from the…
We give a detailed analysis of pairs of vector and hypermultiplet theories with N=2 supersymmetry in four spacetime dimensions that are related by the (classical) mirror map. The symplectic reparametrizations of the special K\"ahler space…
We construct the hyper-K\"ahler moduli space of framed monopoles over $\mathbb{R}^3$ for any connected, simply connected, compact, semisimple Lie group and arbitrary mass and charge, and hence symmetry breaking. In order to do so, we define…
We describe moduli spaces of invariant generalized complex structures and moduli spaces of invariant generalized K\"ahler structures on maximal flag manifolds under $B$-transformations. We give an alternative description of the moduli space…
We show how to compute terms in an expansion of the world-volume superpotential for fairly general D-branes on the quintic Calabi-Yau using linear sigma model techniques, and show in examples that this superpotential captures the geometry…
We study analysis over infinite dimensional manifolds consisted by sequences of almost Kaehler manifolds. We develop moduli theory of pseudo holomorphic curves into such spaces with high symmetry. Many mechanisms of the standard moduli…
Generalized Calabi-Gray manifolds are non-K\"ahler complex manifolds with very explicit geometry yet not being homogeneous. In this note, we demonstrate that how generalized Calabi-Gray manifolds can be used to answer some questions in…
We study the geometry of the leaf closure space of regular and singular Riemannian foliations. We give conditions which assure that this leaf space is a singular symplectic or K\"ahler space.
We construct K\"ahler groups with arbitrary finiteness properties by mapping products of closed Riemann surfaces holomorphically onto an elliptic curve: for each $r\geq 3$, we obtain large classes of K\"ahler groups that have classifying…
We survey our recent new results on the geometry of Teichmuller and moduli spaces of Riemann surfaces and Calabi-Yau manifolds.
In this paper, we prove a transversality theorem for the moduli space of perturbed special Lagrangian submanifolds in a 6-dimensional manifold equipped with a generalization of a Calabi-Yau structure. These perturbed special Lagrangian…
The Kahler potential is the least understood part of effective N=1 supersymmetric theories derived from string compactifications. Even at tree-level, the Kahler potential for the physical matter fields, as a function of the moduli fields,…
This article first reviews the calculation of the N = 1 effective action for generic type IIA and type IIB Calabi-Yau orientifolds in the presence of background fluxes by using a Kaluza-Klein reduction. The Kahler potential, the gauge…
We review an approach for computing non-perturbative, exact superpotentials for Type II strings compactified on Calabi-Yau manifolds, with extra fluxes and D-branes on top. The method is based on an open string generalization of mirror…
For any Lagrangean K\"ahler submanifold $M \subset T^*{\Bbb C}^n$, there exists a canonical hyper K\"ahler metric on $T^*M$. A K\"ahler potential for this metric is given by the generalized Calabi Ansatz of the theoretical physicists…
We study the geometry of the scalar manifolds emerging in the no-scale sector of Kahler moduli and matter fields in generic Calabi-Yau string compactifications, and describe its implications on scalar masses. We consider both heterotic and…
On a compact complex manifold $(M, J)$ endowed with a holomorphic Poisson tensor $\pi_J$ and a deRham class $\alpha\in H^2(M, \mathbb R)$, we study the space of generalized K\"ahler (GK) structures defined by a symplectic form $F\in \alpha$…
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…
This thesis was motivated by a desire to understand the natural geometry of hyperbolic monopole moduli spaces. We take two approaches. Firstly we develop the twistor theory of singular hyperbolic monopoles and use it to study the geometry…