arXiv subjects
Publications and source records attributed to Henrique Sá Earp.
We revisit the study of $G_2$-structures with special torsion, and isolated singularities. Many of the known examples with conical singularities admit additional symmetries, and we describe circle-invariant $G_2$-structures in this context. Finally, we show that collapsing the circle fibres of a contact Calabi-Yau manifold at isolated points cannot produce a $G_2$-structure with bounded torsion.
The heterotic $SU(3)$ system, also known as the Hull--Strominger system, arises from compactifications of heterotic string theory to six dimensions. This paper investigates the local structure of the moduli space of solutions to this system on a compact 6-manifold $X$, using a vector bundle $Q=(T^{1,0}X)^* \oplus {End}(E) \oplus T^{1,0}X$, where $E\to X$ is the classical gauge bundle arising in the system. We establish that the moduli space has an expected dimension of zero. We achieve this by studying the deformation complex associated to a differential operator $\bar{D}$, which emulates a holomorphic structure on $Q$, and demonstrating an isomorphism between the two cohomology groups which govern the infinitesimal deformations and obstructions in the deformation theory for the system. We also provide a Dolbeault-type theorem linking these cohomology groups to Čech cohomology, a result which might be of independent interest, as well as potentially valuable for future research.
How can a National Artificial Intelligence Strategy be effectively monitored? To address this question, we propose a methodology consisting of two key components. First, it involves identifying relevant indicators within national AI strategies. Second, it assesses the alignment between these indicators and the strategic actions of a specific government's AI strategy, allowing for a critical evaluation of its monitoring measures. Moreover, identifying these indicators helps assess the overall quality of the strategy's structure. A lack of alignment between strategic actions and the identified indicators may reveal gaps or blind spots in the strategy. This methodology is demonstrated using the Brazilian AI strategy as a case study.
We introduce a method to construct $G_2$-instantons over compact $G_2$-manifolds arising as the twisted connected sum of a matching pair of building blocks [Kov03,KL11,CHNP12]. Our construction is based on gluing $G_2$-instantons obtained from holomorphic bundles over the building blocks via the first named author's work [SE11]. We require natural compatibility and transversality conditions which can be interpreted in terms of certain Lagrangian subspaces of a moduli space of stable bundles on a K3 surface.
We give a simple direct proof of uniqueness of tangent cones for singular projectively Hermitian Yang-Mills connections on reflexive sheaves at isolated singularities modelled on $μ$-polystable holomorphic bundles over $\mathbf{P}^{n-1}$.