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: pg(X,E) ≥ hn-r,0(X). 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.
@article{urn:eudml:doc:44367,
title = {Geometric genera for ample vector bundles with regular sections.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {13},
year = {2000},
pages = {33-48},
zbl = {0993.14003},
mrnumber = {MR1794902},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44367}
}
Lanteri, Antonio. Geometric genera for ample vector bundles with regular sections.. Revista Matemática de la Universidad Complutense de Madrid, Tome 13 (2000) pp. 33-48. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44367/