Summary: manuscripta mathematica manuscript No.
(will be inserted by the editor)
Characterization theorems for the projective
space and vector bundle adjunction.
Received: date / Revised version: date
Abstract. We consider some conditions under which a smooth projective variety
X is actually the projective space. We also extend to the case of positive charac-
teristic some results in the theory of vector bundle adjunction. We use methods
and techniques of the so called Mori theory, in particular the study of rational
curves on projective manifolds.
Mathematics Subject Classication (1991): 14E30, 14J40, 14J45
Let X be a smooth projective variety of dimension n, dened over an
algebraically closed eld k; we denote by TX its tangent bundle and by
KX = det(T X) its canonical bundle.
A natural problem is to nd simple conditions under which the manifold
X is actually the projective space P n . A very famous one is given by the
following theorem of S. Mori (see ).
Theorem. X is the projective space if and only if TX is ample.