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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
Arrondo Esteban, Enrique ; Lanteri, Antonio ; Novelli, Carla | Department of Mathematics, Tokyo Institute of Technology | 2013A notion of "delta-genus" for ample vector bundles g of rank two on a smooth projective threefold X is defined as a couple of integers (delta(1),delta(2)).This extends the classical definition holding for ample line bundles. Then pairs (X, epsil[...]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[...]
