# Vortices, Painlevé integrability and projective geometry

@article{Contatto2018VorticesPI, title={Vortices, Painlevé integrability and projective geometry}, author={Felipe Contatto}, journal={arXiv: Mathematical Physics}, year={2018} }

The first half of the thesis concerns Abelian vortices and Yang-Mills (YM) theory. It is proved that the 5 types of vortices recently proposed by Manton are symmetry reductions of (A)SDYM equations with suitable gauge groups and symmetry groups acting as isometries in a 4-manifold. As a consequence, the twistor integrability results of such vortices can be derived. It is presented a natural definition of their kinetic energy and thus the metric of the moduli space was calculated by the Samols…

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