Let X be a smooth complex projective variety of dimension n \geq 2. A notion of geometric genus p_g(X,E) for ample vector bundeles E of rank r < n on X admitting some regular sections is introduced. The following inequality holds: p_g(X,E) \geq h^{n-r,0}(X). The question of characterizing equalityis discussed and the answer is given for E decomposable of corank 2. Some conjectures suggested by the result are formulated.

Geometric genera for ample vector bundles with regular sections / A. Lanteri. - In: REVISTA MATEMATICA COMPLUTENSE. - ISSN 1139-1138. - 13:1(2000), pp. 33-48.

### Geometric genera for ample vector bundles with regular sections

#### Abstract

Let X be a smooth complex projective variety of dimension n \geq 2. A notion of geometric genus p_g(X,E) for ample vector bundeles E of rank r < n on X admitting some regular sections is introduced. The following inequality holds: p_g(X,E) \geq h^{n-r,0}(X). The question of characterizing equalityis discussed and the answer is given for E decomposable of corank 2. Some conjectures suggested by the result are formulated.
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ample vectoe bundles ; geometric genus ; adjunction
Settore MAT/03 - Geometria
http://dmle.cindoc.csic.es/pdf/REVISTAMATEMATICACOMPLUTENSE_2000_13_01_02.pdf
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/178617
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