 
Summary: Special rays in the Mori cone
of a projective variety
Marco Andreatta
Mathematics Subject Classication: Primary 14E30; Secondary 14J40.
Key words and phrases: Projective varieties, Rational curves, Extremal rays,
Mori theory.
The text of the conference is on the web page
http://www.science.unitn.it/ andreatt
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2 M. Andreatta
1 Introduction
Let X be a smooth ndimensional projective variety over an algebraically closed
eld k of arbitrary characteristic.
In 1978 Mori proved the so called FrenkelHartshorne conjecture who states the
following:
Theorem 1.1 TX is ample if and only if X = P n .
in the case of characteristic zero the Frenkel formulation is the following:
Theorem 1.2 A compact complex manifold X admits a kahler metric whose
holomorphic bisectional curvature is positive i X = P n .
