Related papers: Moduli Spaces of Contact Instantons

We give a correspondence between toric 3-Sasaki 7-manifolds S and certain toric Sasaki-Einstein 5-manifolds M. These 5-manifolds are all diffeomorphic to k#(S^2\times S^3), where k=2b_2(S)+1, and are given by a pencil of Sasaki embeddings…

Following an earlier paper on the differential-geometric structure of the moduli space of special Lagrangian submanifolds in a Calabi-Yau manifold, we follow an analogous approach for compact complex Lagrangian submanifolds of a…

We study the Lie algebra of infinitesimal isometries on compact Sasakian and K--contact manifolds. On a Sasakian manifold which is not a space form or 3--Sasakian, every Killing vector field is an infinitesimal automorphism of the Sasakian…

We describe mirror manifolds in dimensions different from the familiar case of complex threefolds. We emphasize the simplifying features of dimension three and supply more robust methods that do not rely on such special characteristics and…

We use the gauged linear sigma model introduced by Witten to calculate instanton expansions for correlation functions in topological sigma models with target space a toric variety $V$ or a Calabi--Yau hypersurface $M \subset V$. In the…

We describe explicitly the moduli spaces $M^{pst}_g(S,E)$ of polystable holomorphic structures $E$ with $\det E\cong K$ on a rank 2 vector bundle $E$ with $c_1(E)=c_1(K)$ and $c_2(E)=0$ for all minimal class VII surfaces $S$ with $b_2(S)=1$…

By using the so-called Information Metric on the moduli space of an anti-selfdual (ASD) Instanton in a Self-Dual (SD) Non-Commutative background, we investigate the geometry of moduli space. The metric is evaluated perturbatively in…

Many authors have studied Ricci solitons and their analogs within the framework of (almost) contact geometry. In this article, we thoroughly study the $(m,\rho)$-quasi-Einstein structure on a contact metric manifold. First, we prove that if…

We construct a metric on the moduli space of bodies in Euclidean space. The moduli space is defined as the quotient space with respect to the action of integral affine transformations. This moduli space contains a subspace, the moduli space…

Expressions for the number of moduli of arbitrary SU(n) vector bundles constructed via Fourier-Mukai transforms of spectral data over Calabi- Yau threefolds are derived and presented. This is done within the context of simply connected,…

These are notes of my lectures given at the school on intersection theory and moduli at the ICTP, Trieste. We construct moduli spaces of K3 surfaces and higherdimensional hyperkaehler manifolds, including moduli spaces of (2,2)-conformal…

We examine the dynamics of noncommutative instantons of instanton number $2$ and commutative instantons of instanton number $3$ in 5d Super Yang Mills theory. We begin by detailing the construction of the 1/4-BPS instanton solutions, their…

We present a novel approach to the study of Yang-Mills instantons on quaternionic K\"ahler manifolds, based on an extension of the harmonic space method of constructing instantons on hyperk\"ahler manifolds. Our results establish a…

We study the mirrors of five-parameter Calabi-Yau threefolds first studied by Hulek and Verrill in the context of observed modular behaviour of the zeta functions for Calabi-Yau manifolds. Toric geometry allows for a simple explicit…

In this paper we construct various moduli spaces of K3 surfaces $M$ equipped with a surjective holomorphic map $\pi:M\to\Pb^1$ with generic fiber a complex torus (e.g., an elliptic fibration). Examples include moduli spaces of such maps…

We classify locally the contact metric (k,mu)-spaces whose Boeckx invariant is $\le -1$ as tangent hyperquadric bundles of Lorentzian space forms.

Let $X$ be a compact connected Riemann surface of genus $g$, with $g\geq 2$, and ${\cal M}_{\xi}$ a smooth moduli space of fixed determinant semistable vector bundles of rank $n$, with $n\geq 2$, over $X$. Take a smooth anticanonical…

In this paper we study the interplay between complex coordinates on the Calabi-Yau metric cone and the special Killing forms on the toric Sasaki-Einstein manifold. In the general case we give a procedure to locally construct the special…

This paper concerns orientability of moduli spaces of Spin(7)-instantons on compact 8-manifolds $X$ with Spin(7)-structure for the Lie groups SU($m$) and U($m$), and of moduli spaces of coherent sheaves on Calabi-Yau 4-folds. Such…

We construct proper moduli algebraic spaces of K-polystable $\mathbb{Q}$-Fano cones (a.k.a. Calabi-Yau cones) or equivalently their links i.e., Sasaki-Einstein manifolds with singularities. As a byproduct, it gives alternative algebraic…