THE KODAIRA DIMENSION OF A GRAVITATIONAL MONOPOLE

Gourab Bhattacharya (1)

1 LAG - Laboratoire Alexander Grothendieck

This article is a step forward to prove the existence of the solution of the Gravitational monopole equations. We show using simple arguments that surfaces of Kähler type of Kodaira dimension ≥ 0 can be a solution of the Gravitational monopole equation, in particular the complex elliptic surfaces of Kodaira dimension 0 or 1 are the possible candidates.

Domains: Mathematical Physics [math-ph]; Algebraic Geometry [math.AG]; Differential Geometry [math.DG]; High Energy Physics - Theory [hep-th]; Physics [physics]; Mathematics [math]

Gourab Bhattacharya. THE KODAIRA DIMENSION OF A GRAVITATIONAL MONOPOLE: A step towards the existence of a solution to the Gravitational Monopole Equations.. 2022. ⟨hal-03898609⟩