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
A. LanteriPrimo
2000
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.File in questo prodotto:
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