Summary: The projective space
M. Andreatta
Universita di Trento, Italy
www.science.unitn.it/~ andreatt

Notations
X = smooth projective variety of dimension n,
TX = tangent bundle and
K X = det(TX) canonical bundle.
Problem
Find simple conditions under which the mani-
fold X is actually the projective space P
n .
A very famous condition is the following, con-
jectured by Frenkel and Hartshorne:
Theorem [Mori; 79]. X is the projective
space if and only if TX is ample.
One of the big idea introduced by Mori is the
fact of using rational curves on Fano mani-
folds. With this tecnique many results were

Source: Andreatta, Marco - Dipartimento di Matematica, Università di Trento

Collections: Mathematics