Related papers: Resolving Singularities in (0,2) Models

We describe a class of supersymmetric gauged linear sigma-model, whose target space is the infinite dimensional space of bundles on a Calabi-Yau 3- or 2-fold. This target space can be considered the configuration space of D-branes wrapped…

We use the method of stable degenerations to study the local geometry of Calabi-Yau fourfolds for F-theory compactifications dual to heterotic compactifications on a Calabi-Yau threefold with fivebranes wrapping holomorphic curves in the…

Holomorphic gauge fields in N=1 supersymmetric heterotic compactifications can constrain the complex structure moduli of a Calabi-Yau manifold. In this paper, the tools necessary to use holomorphic bundles as a mechanism for moduli…

We study (0,2) deformations of N=2 Liouville field theory and its mirror duality. A gauged linear sigma model construction of the ultraviolet theory connects (0,2) deformations of Liouville field theory and (0,2) deformations of N=2…

We initiate a systematic investigation of F-theory on elliptic fibrations with singularities which cannot be resolved without breaking the Calabi-Yau condition, corresponding to $\mathbb Q$-factorial terminal singularities. It is the…

We consider the general case of a type IIA string compactified on a Calabi-Yau manifold which has a heterotic dual description. It is shown that the nonabelian gauge symmetries which can appear nonperturbatively in the type II string but…

In this paper we propose a unified approach to (topological) string theory on certain singular spaces in their large volume limit. The approach exploits the non-commutative structure of D-branes, so the space is described by an algebraic…

We propose a class of N=2 supersymmetric nonlinear sigma models on the noncompact Ricci-flat Kahler manifolds, interpreted as the complex line bundles over the hermitian symmetric spaces. Kahler potentials and Ricci-flat metrics for these…

In a previous publication, arXiv:1106.4804, we have found 200 models from heterotic Calabi-Yau compactifications with line bundles, which lead to standard models after taking appropriate quotients by a discrete symmetry and introducing…

Heterotic compactifications on Calabi-Yau threefolds frequently exhibit textures of vanishing Yukawa couplings in their low energy description. The vanishing of these couplings is often not enforced by any obvious symmetry and appears to be…

We survey what is known about singularities of special Lagrangian submanifolds (SL m-folds) in (almost) Calabi-Yau manifolds. The bulk of the paper summarizes the author's five papers math.DG/0211294, math.DG/0211295, math.DG/0302355,…

We study a class of extremal transitions between topological distinct Calabi--Yau manifolds which have an interpretation in terms of the special massless states of a type II string compactification. In those cases where a dual heterotic…

We study the degenerating limits of superconformal theories for compactifications on singular K3 and Calabi-Yau threefolds. We find that in both cases the degeneration involves creating an Euclidean two-dimensional black hole coupled weakly…

We consider four dimensional heterotic compactifications on smooth elliptic Calabi-Yau threefolds. Using spectral cover techniques, we study bundle cohomology groups corresponding to charged matter multiplets. The analysis shows that in…

We consider the singuralities of 2-dimensional moduli spaces of semi-stable sheaves on K3 surfaces. We show that the moduli space is normal, in particular the singuralities are rational double points. We also describe the exceptional locus…

A brief review of some aspects of heterotic (0,2) compactifications in the framework of exactly solvable superconformal field theories and gauged linear sigma models is presented.

We study the low energy behaviour of N=(2,2) supersymmetric gauge theories in 1+1 dimensions, with orthogonal and symplectic gauge groups and matters in the fundamental representation. We observe supersymmetry breaking in super-Yang-Mills…

We consider four-dimensional supersymmetric compactifications of the E8 x E8 heterotic string on Calabi-Yau manifolds endowed with vector bundles with structure group SU(N) x U(1) and five-branes. After evaluating the Green-Schwarz…

The goal of this paper is to generalize results concerning the deformation theory of Calabi-Yau and Fano threefolds with isolated hypersurface singularites, due to the first author, Namikawa and Steenbrink. In particular, under the…

In the first part of this thesis, we study the Yamabe problem with singularities, that we can announce as follow: Given a compact Riemannian manifold $(M,g)$, find a constant scalar curvature metric, conformal to $g$, when $g$ has not…