Holomorphic bundles for higher dimensional gauge theory

Author(s)

Jardim, Marcos ; Menet, Gregoire ; Prata, Daniela M. ; Sa Earp, Henrique N.

• Document type: Journal article
• Source: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY; v. 49, n. 1, p. 117-132, FEB 2017.
• Web of Science Citations: 1

Abstract

Motivated by gauge theory under special holonomy, we present techniques to produce holomorphic bundles over certain non-compact 3-folds, called building blocks, satisfying a stability condition `at infinity'. Such bundles are known to parametrize solutions of the Yang-Mills equation over the G2-manifolds obtained from asymptotically cylindrical Calabi-Yau 3-folds studied by Kovalev, Haskins et al. and Corti et al. The most important tool is a generalization of Hoppe's stability criterion to holomorphic bundles over smooth projective varieties X with PicX similar or equal to Z(l), a result which may be of independent interest. Finally, we apply monads to produce a prototypical model of the curvature blow-up phenomenon along a sequence of asymptotically stable bundles degenerating into a torsion-free sheaf. (AU)

• FAPESP's process: 14/05733-9 - Geometry of irreducible symplectic varieties
• Grantee: Grégoire Menet
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 11/21398-7 - Stable vector bundles on Pn, cohomology of monads and quiver representations.
• Grantee: Daniela Moura Prata dos Santos
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 14/14743-8 - Sheaves on projective varieties
• Grantee: Marcos Benevenuto Jardim
• Support Opportunities: Regular Research Grants
• FAPESP's process: 14/24727-0 - G2-instantons over twisted connected sums
• Grantee: Henrique Nogueira de Sá Earp
• Support Opportunities: Regular Research Grants
• FAPESP's process: 09/10067-0 - Instantons over G2-manifolds
• Grantee: Henrique Nogueira de Sá Earp
• Support Opportunities: Scholarships in Brazil - Post-Doctoral