Projective surfaces with $ k −veryamplelinebundlesofdegree-very ample line bundles of degree −veryamplelinebundlesofdegree\ leq 4k+ 4$ (original) (raw)

On the 2 very ampleness of the adjoint bundle

Manuscripta Mathematica, 1991

With an Appendix by E. Ballico Let S be a smooth projective surface over C polarized by a 2-very ample line bundle L=Os(L), i.e. for any 0-dimensional subscheme (Z,Oz) of length 3 the restriction map F(L)--->F(L| is a surjection. This generalization of very ampleness was recently introduced by M. Beltrametti and A.J. Sommese. The authors prove that, if L.L > 13, the adjoint line bundle Ks| is 2-very ample apart from a list of well understood exceptions and up to contracting down the smooth rational curves E such that E.E = -1, L.E = 2.

A criterion for ample vector bundles over a curve in positive characteristic

Bulletin des Sciences Mathématiques, 2005

Let X be a smooth projective curve defined over an algebraically closed field of positive characteristic. We give a necessary and sufficient condition for a vector bundle over X to be ample. This generalizes a criterion given by Lange in [Math. Ann. 238 (1978) 193-202] for a rank two vector bundle over X to be ample.

Martens-Mumford theorems for Brill-Noether schemes arising from very ample line bundles

Archiv der Mathematik, 2015

Tangent spaces of V r d (L)'s, specific subschemes of C d arising from various line bundles L on C, are described. Then we proceed to prove Martens theorem for these schemes, by which we determine curves C, which for some very ample line bundle L on C and some integers r and d with d ≤ h 0 (L) − 2, the scheme V r d (L) might attain its maximum dimension.

On positivity of line bundles on Enriques surfaces

We study linear systems on Enriques surfaces. We prove rationality of Seshadri constants of ample line bundles on Enriques surfaces and provide lower bounds on these numbers. We show the nonexistence of k-very ample line bundles on Enriques surfaces of degree 4k + 4 for k ≥ 1, thus answering an old question of Ballico and Sommese.

Peculiar loci of ample and spanned line bundles

manuscripta mathematica, 2003

The bad locus and the rude locus of an ample and base point free linear system on a smooth complex projective variety are introduced and studied. Polarized surfaces of small degree, or whose degree is the square of a prime, with nonempty bad loci are completely classified. Several explicit examples are offered to describe the variety of behaviors of the two loci.