Let E be an ample and spanned vector bundle of rank r \geq 2 on a smooth complex propjective surface X and set L = \det E. We show that K_X+L is spanned except for (X,E)=(P^2, O(1)^{\oplus 2}) and we describe all pairs (X,E) for which K_X+det E fais to be very ample.

Adjoint bundles of ample and spanned vector bundles on algebraic surfaces / A. Lanteri, H. Maeda. - In: JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK. - ISSN 0075-4102. - 1992:433(1992), pp. 181-199. [10.1515/crll.1992.433.181]

### Adjoint bundles of ample and spanned vector bundles on algebraic surfaces

#### Abstract

Let E be an ample and spanned vector bundle of rank r \geq 2 on a smooth complex propjective surface X and set L = \det E. We show that K_X+L is spanned except for (X,E)=(P^2, O(1)^{\oplus 2}) and we describe all pairs (X,E) for which K_X+det E fais to be very ample.
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projective algebraic surface; ample and spanned vector bundle; adjunction theory; Reider's theorem; classification
Settore MAT/03 - Geometria
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