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Let Hilb d P 2 =Hilb d P 2 C denote the Hilbert scheme parametrizing 0-dimensional, length-d subschemes of the plane. The authors determine an additive basis for the Chow group A.(Hilb d P 2 ) consisting of classes of closures of locally clo[...]texto impreso
For a variety X?PN, its mth order dual variety is the variety X?m?(PN)? consisting of hyperplanes containing an mth osculating space of X. The strict dual variety X? is the smallest nonempty X?m. All these dual varieties were described by Piene [...]texto impreso
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We prove that, if a smooth complex projective surface S subset of P-N is k-regular, then its k-th order dual variety has the expected dimension, except if S is the k-th Veronese surface. This answers positively a conjecture stated in a previous [...]texto impreso
We investigate higher order dual varieties of projective manifolds whose osculatory behavior is the best possible, in particular, for a k-jet ample surface we prove the nondegeneratedness of the k-th dual variety and for 2-regular surfaces we in[...]texto impreso
Lanteri, Antonio ; Mallavibarrena Martínez de Castro, Raquel ; Piene, Ragni | Academic Press | 2015-11-01Quadric flbrations over smooth curves are investigated with respect to their osculatory behavior. In particular, bounds for the dimensions of the osculating spaces are determined, and explicit formulas for the classes of the inflectional loci ar[...]texto impreso
Let X?PN be a scroll over a smooth curve C and let L=OPN(1)|X denote the hyperplane bundle. The special geometry of X implies that certain sheaves related to the principal part bundles of L are locally free. The inflectional loci of X can be exp[...]texto impreso
Lanteri, Antonio ; Mallavibarrena Martínez de Castro, Raquel ; Piene, Ragni | Indiana University | 2012Let X subset of P-N be a scroll over an m-dimensional variety Y. We find the locally free sheaves on X governing the osculating behavior of X, and, under certain dimension assumptions, we compute the cohomology class and the degree of the inflec[...]texto impreso
In the paper under review, the authors study the jets of antimulticanonical bundles on certain del Pezzo surfaces. The main idea is to investigate the stratification of the surfaces given by the rank of the evaluation map with values in the seco[...]texto impreso
The main objects of this paper are osculating spaces of order m to smooth algebraic curves, with the property of meeting the curve again. We prove that the only irreducible curves with an infinite number of this type of osculating spaces of orde[...]texto impreso
Osculating spaces of decomposable scrolls (of my genus and not necessarily normal) arc studied and their inflectional loci are related to those of their generating curves by using systematically an idea introduced by Piene and Sacchiero in the s[...]texto impreso
Smooth projective surfaces fibered in conics over a smooth curve are investigated with respect to their k-th osculatory behavior. Due to the bound for the dimension of their osculating spaces they do not differ at all from a general surface for [...]texto impreso
Let X be a projective manifold, embedded via a line bundle L. For any point x?X the k-th projective tangent bundle is defined as Tk,x=P(H0(L/mk+1x)). There is a natural map jk from the global sections H0(L) to Tk,x, assigning to each section its[...]texto impreso
Arrondo Esteban, Enrique ; Mallavibarrena Martínez de Castro, Raquel ; Sols, Ignacio | Springer | 1990The purpose of the paper under review is to give a proof of six formulas by Schubert (two of which he proved and four of which he only conjectured) concerning the number of double contacts among the curves of two families of plane curves. The me[...]texto impreso
G. Ellingsrud and S. A. Strømme [Invent. Math. 87 (1987), no. 2, 343–352; see the following review] have proved that the Chow group of the Hilbert scheme Hilb d P 2 is free and have computed the ranks of its homogeneous parts A i (Hilb d P 2 )[...]
