92 citations · 391 across the 27 of their papers we have counts for
34 papers
Cohomogeneity one solutions of the IIB system
Lorenzo Foscolo, Mario Garcia-Fernandez
The IIB system is a system of PDEs for an SU(3)--structure and a positive function on a 6-manifold. Its solutions describe conformally balanced pluriclosed Hemitian metrics on comp…
Universal Hitchin moduli spaces
Luis Álvarez-Cónsul, Mario Garcia-Fernandez, Oscar García-Prada +1
We study metric aspects of the universal moduli space of solutions to Hitchin's equations as the complex structure varies over the Teichmüller space of a closed s…
-structures with torsion and the deformed Shatashvili-Vafa vertex algebra
Andoni De Arriba de La Hera, Mateo Galdeano, Mario Garcia-Fernandez
We construct representations of the deformed Shatashvili-Vafa vertex algebra , with parameter , as recently proposed in the physics literature by F…
Vertex algebras from the Hull-Strominger system
Luis Álvarez-Cónsul, Andoni De Arriba de La Hera, Mario Garcia-Fernandez
Motivated by the programme on mirror symmetry for non-Kähler manifolds, we construct representations of the superconformal vertex algebra associated to solutions of the Hull-…
Futaki Invariants and Yau's Conjecture on the Hull-Strominger system
Mario Garcia-Fernandez, Raul Gonzalez Molina
We find a new obstruction to the existence of solutions of the Hull-Strominger system, which goes beyond the balanced property of the Calabi-Yau manifold and the Mumford-Ta…
Harmonic metrics for the Hull-Strominger system and stability
Mario Garcia-Fernandez, Raul Gonzalez Molina
We investigate stability conditions related to the existence of solutions of the Hull-Strominger system with prescribed balanced class. We build on recent work by the authors, wher…
Obstructions to the existence of solutions of the self-dual Einstein-Maxwell-Higgs equations on a compact surface
Luis Álvarez-Cónsul, Mario Garcia-Fernandez, Oscar García-Prada +2
In this note we present an obstruction to the existence of solutions to the self-dual Einstein-Maxwell-Higgs equations on a compact surface, which depends on the multiplicities of…
Non-Kähler Calabi-Yau geometry and pluriclosed flow
Mario Garcia-Fernandez, Joshua Jordan, Jeffrey Streets
Hermitian, pluriclosed metrics with vanishing Bismut-Ricci form give a natural extension of Calabi-Yau metrics to the setting of complex, non-Kähler manifolds, and arise independen…
(0,2) Mirror Symmetry on homogeneous Hopf surfaces
Luis Álvarez-Cónsul, Andoni De Arriba de La Hera, Mario Garcia-Fernandez
In this work we find the first examples of (0,2) mirror symmetry on compact non-Kähler complex manifolds. For this we follow Borisov's approach to mirror symmetry using vertex alge…
Generalized Ricci Flow
Mario Garcia-Fernandez, Jeffrey Streets
This book gives an introduction to fundamental aspects of generalized Riemannian, complex, and Kähler geometry. This leads to an extension of the classical Einstein-Hilbert action,…
-Dual solutions and infinitesimal moduli of the -Strominger system
Andrew Clarke, Mario Garcia-Fernandez, Carl Tipler
We consider -structures with torsion coupled with -instantons, on a compact -dimensional manifold. The coupling is via an equation for -forms which appears in super…
Gauge theory for string algebroids
Mario Garcia-Fernandez, Roberto Rubio, Carl Tipler
We introduce a moment map picture for holomorphic string algebroids where the Hamiltonian gauge action is described by means of inner automorphisms of Courant algebroids. The zero…
Gravitating vortices with positive curvature
Mario Garcia-Fernandez, Vamsi Pritham Pingali, Chengjian Yao
We give a complete solution to the existence problem for gravitating vortices with non-negative topological constant . Our first main result builds on previous resul…
T-dual solutions of the Hull-Strominger system on non-Kähler threefolds
Mario Garcia-Fernandez
We construct new examples of solutions of the Hull-Strominger system on non-Kähler torus bundles over K3 surfaces, with the property that the connection on the tangent bun…
On the Kähler-Yang-Mills-Higgs equations
Luis Álvarez-Cónsul, Mario Garcia-Fernandez, Oscar García-Prada
In this paper we introduce a set of equations on a principal bundle over a compact complex manifold coupling a connection on the principal bundle, a section of an associated bundle…
Holomorphic string algebroids
Mario Garcia-Fernandez, Roberto Rubio, Carl Tipler
We introduce the category of holomorphic string algebroids, whose objects are Courant extensions of Atiyah Lie algebroids of holomorphic principal bundles, as considered by Bressle…
Canonical metrics on holomorphic Courant algebroids
Mario Garcia-Fernandez, Roberto Rubio, C. S. Shahbazi +1
The solution of the Calabi Conjecture by Yau implies that every Kähler Calabi-Yau manifold admits a metric with holonomy contained in , and that these metrics a…
Ricci flow, Killing spinors, and T-duality in generalized geometry
Mario Garcia-Fernandez
We introduce a notion of Ricci flow in generalized geometry, extending a previous definition by Gualtieri on exact Courant algebroids. Special stationary points of the flow are giv…
Lectures on the Strominger system
Mario Garcia-Fernandez
These notes give an introduction to the Strominger system of partial differential equations, and are based on lectures given in September 2015 at the GEOQUANT School, held at the I…
Moduli of structures and the Strominger system in dimension 7
Andrew Clarke, Mario Garcia-Fernandez, Carl Tipler
We consider structures with torsion coupled with -instantons, on a compact -dimensional manifold. The coupling is via an equation for -forms which appears in super…
Gravitating vortices and the Einstein--Bogomol'nyi equations
Luis Álvarez-Cónsul, Mario Garcia-Fernandez, Oscar García-Prada +1
In this work we consider the gravitating vortex equations. These equations couple a metric over a compact Riemann surface with a hermitian metric over a holomorphic line bundle equ…
Quantization of Hitchin's equations for Higgs Bundles I
Mario Garcia-Fernandez, Julien Keller, Julius Ross
We provide an algebraic framework for quantization of Hermitian metrics that are solutions of the Hitchin equation for Higgs bundles over a projective manifold. Using Geometric Inv…
Gravitating vortices, cosmic strings, and the Kähler--Yang--Mills equations
Luis Álvarez-Cónsul, Mario Garcia-Fernandez, Oscar García-Prada
In this paper we construct new solutions of the Kahler-Yang-Mills equations, by applying dimensional reduction methods to the product of the complex projective line with a compact…
Self-dual generalized metrics for pure six-dimensional Supergravity
M. Garcia-Fernandez, C. S. Shahbazi
We geometrize six-dimensional pure Supergravity by means of an exact Courant algebroid, whose Severa class is defined through the Supergravity three-form , equip…