Full paper in PDF:
$%A. Lanteri, Geometric genera for ample vector bundles, Rev. Mat. Complut. 13 (2000), no. 1, 33–48.%$

Geometric Genera for Ample Vector Bundles
Antonio LANTERI
Dipartimento di Matematica “F. Enriques”
Università, Via C. Saldini 50
I-20133 Milano — Italy
lanteri@vmimat.mat.unimi.it

Received: February 12, 1999
Revised: June 7, 1999

ABSTRACT

Let X be a smooth complex projective variety of dimension n > 3 . A notion of geometric genus pg(X,E) for ample vector bundles E of rank r < n on X admitting some regular sections is introduced. The following inequality holds: p(X,E) > hn- r,0(X) g . The question of characterizing equality is discussed and the answer is given for E decomposable of corank 2. Some conjectures suggested by the result are formulated.

1991 Mathematics Subject Classification: primary 14F05, 14C20; secondary 14J40.