Carl Tipler

Infinitesimal moduli for the Strominger system and Killing spinors in generalized geometry

We construct the space of infinitesimal variations for the Strominger system and an obstruction space to integrability, using elliptic operator theory. We initiate the study of the geometry of the moduli space, describing the infinitesimal structure of a natural foliation on this space. The associated leaves are related to generalized geometry and correspond to moduli spaces of solutions of suitable Killing spinor equations on a Courant algebroid. As an application, we propose a unifying framework for metrics with holonomy

Deformation of extremal metrics, complex manifolds and the relative Futaki invariant

\mathrm {SU}(3)

Infinitesimal moduli for the Strominger system and generalized Killing spinors

SU(3) and solutions of the Strominger system.

Extremal metrics and lower bound of the modified K-energy

Let X be a compact toric extremal Kähler manifold. Using the work of Székelyhidi (Am. J. Math. 132(4):1077–1090, 2010), we provide a combinatorial criterion on the fan describing X to ensure the existence of complex deformations of X that carry extremal metrics. As an example, we find new CSC metrics on 4-points blow-ups of

Moduli of

\mathbb{C}\mathbb{P}^{1}\times \mathbb{C}\mathbb{P}^{1}

G_2

.

structures and the Strominger system in dimension 7

Let