Classification problems and moduli spaces of geometric structures via Lie Theory
Geometric flows of G2-structures, and their Yang-Mills connections.
Differential topology and topological methods for the study of differential equati...
Full text | |
Author(s): |
Biswas, Indranil
;
Bruzzo, Ugo
;
Grana Otero, Beatriz
;
Lo Giudice, Alessio
Total Authors: 4
|
Document type: | Journal article |
Source: | ASIAN JOURNAL OF MATHEMATICS; v. 20, n. 5, p. 989-1000, 2016. |
Web of Science Citations: | 0 |
Abstract | |
Let X be a compact connected Kahler-Einstein manifold with c(1)(TX) >= 0. If there is a semistable Higgs vector bundle (E, theta) on X with. theta not equal 0, then we show that c(1)(TX) = 0; any X satisfying this condition is called a Calabi-Yau manifold, and it admits a Ricci-flat Kahler form {[}Ya]. Let (E, theta) be a polystable Higgs vector bundle on a compact Ricci-flat Kahler manifold X. Let h be an Hermitian structure on E satisfying the Yang-Mills-Higgs equation for (E, theta). We prove that h also satisfies the Yang-Mills-Higgs equation for (E, 0). A similar result is proved for Hermitian structures on principal Higgs bundles on X satisfying the Yang-Mills-Higgs equation. (AU) | |
FAPESP's process: | 13/20617-2 - Principal bundles over projective varieties |
Grantee: | Alessio Lo Giudice |
Support Opportunities: | Scholarships in Brazil - Post-Doctoral |