L. Andrianopoli et al., DUALITY COVARIANT FORMULATION OF EXTENDED SUPERGRAVITY - CENTRAL CHARGES, BPS STATES AND BLACK-HOLE ENTROPY, Fortschritte der Physik, 46(3), 1998, pp. 285-323
In these lectures we give a geometrical formulation of N-extended supe
rgravities which generalizes N = 2 special geometry of N = 2 theories.
In all these theories duality symmetries are related to the notion of
''flat symplectic bundles'' and central charges may be defined as ''s
ections'' over these bundles. Attractor points giving rise to ''fixed
scalars'' of the horizon geometry and Bekenstein-Hawking entropy formu
la for extremal black-holes are discussed in some details.