Geometria Torica Simplettica. Introduzione e applicazioni alla Supergravità

We provide an introduction to geometric structures related to Supergravity theories, with particular attention to symplectic toric manifolds. An alternative characterization of these manifolds is discussed using Delzant polytopes and analyzing Delzant’s correspondence theorem. Complex projective spaces and Hirzebruch surfaces are then investigated as significant examples of K¨ahler toric manifolds.