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Journals and Conferences
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… (More)
Hilbert schemes of suitable smooth, projective manifolds of low degree which are 3-fold scrolls over the Hirzebruch surface F1 are studied. An irreducible component of the Hilbert scheme parametrizing such varieties is shown to be generically smooth of the expected dimension and the general point of such a component is described.
The Hilbert scheme of 3-folds in P, n ≥ 6, that are scrolls over P or over a smooth quadric surface Q ⊂ P or that are quadric or cubic fibrations over P is studied. All known such threefolds of degree 7 ≤ d ≤ 11 are shown to correspond to smooth points of an irreducible component of their Hilbert scheme, whose dimension is computed.
Very ampleness criteria for rank 2 vector bundles over smooth, ruled surfaces over rational and elliptic curves are given. The criteria are then used to settle open existence questions for some special threefolds of low
The conjecture on the (degree − codimension+ 1)regularity of projective varieties is proved for smooth linearly normal polarized varieties (X, L) with L very ample, for low values of ∆(X, L) = degree− codimension− 1. Results concerning the projective normality of some classes of special varieties including scrolls over curves of genus 2 and quadric… (More)
Smooth complex surfaces polarized with an ample and globally generated line bundle of degree three and four, such that the adjoint bundle is not globally generated, are considered. Scrolls of a vector bundle over a smooth curve are shown to be the only examples in degree three. Two classes of examples in degree four are presented, one of which is shown to… (More)
Several families of rank-two vector bundles on Hirzebruch surfaces are shown to consist of all very ample, uniform bundles. Under suitable numerical assumptions, the projectivization of these bundles, embedded by their tautological line bundles as linear scrolls, are shown to correspond to smooth points of components of their Hilbert scheme, the latter… (More)
Let Z be a two dimensional irreducible complex component of the solution set of a system of polynomial equations with real coefficients in N complex variables. This work presents a new numerical algorithm, based on homotopy continuation methods, that begins with a numerical witness set for Z and produces a decomposition into 2-cells of any almost smooth… (More)
Zero-schemes on smooth complex projective varieties, forcing all elements of ample and free linear systems to be reducible are studied. Relationships among the minimal length of such zero-schemes, the positivity of the line bundle associated with the linear system, and the dimension of the variety are established. Bad linear spaces are also investigated.
The projective normality of smooth, linearly normal surfaces of degree 9 in P is studied. All non projectively normal surfaces which are not scrolls over a curve are classified. Results on the projective normality of surface scrolls are also given.