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The projective space M. Andreatta
 

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 one is the following,
(conjectured by Frenkel and Hartshorne):
Theorem [Mori 79].
X = P n if and only if TX is ample.
To prove it Mori introduced the use of :
rational curves on Fano manifolds.
This method has been developed to study
(uniruled) projective manifolds.

  

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

 

Collections: Mathematics