On the index of harmonic maps from surfaces to complex projective spaces

2019/01/31 by Oliver, Joe
#53C43 #58E20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.11475

Abstract

We estimate the dimensions of the spaces of holomorphic sections of certain line bundles to give improved lower bounds on the index of complex isotropic harmonic maps to complex projective space from the sphere and torus, and in some cases from higher genus surfaces.

Related

• The Geometry of the Space of Holomorphic Maps from a Riemann Surface into Complex Projective Space
• The Space of Harmonic Maps from the 2-sphere to the Complex Projective Plane
• Constant energy families of harmonic maps
• Index of minimal spheres and isoperimetric eigenvalue inequalities
• Harmonic tori and generalised Jacobi varieties